Yes, it's grammatical.

No, it is not in good style.

No, you cannot be assured that everyone will process it correctly. Just because something is grammatical doesn't mean everyone will process it well: I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve.

The best way to say their clunky phrase is:

...another verb, (one) whose present tense I've already talked about.

The optional one might be useful in speech to make sure the listener realizes this is a descriptive clause not a restrictive one.

Why the person said the clumsy version instead of the simple and clear — and to my mind obvious — alternative I've proposed we cannot know for certain, but we can make some educated guesses:

1. If you had not made the “But in German this is impossible” proviso, I would have said that her first language might be one where the clumsy way is the only way allowed. Not all languages have single words that work just like whose does in English, or even the wer/wen/wem/wes set of German. If so, said hypothetical speaker might have naturally reached for something more like whatever they're used to, no matter how clumsy that might be in English.
2. She might be suffering under the distressingly widespread misunderstanding that whose is restricted to animates the way who and whom are. It isn't, at least not when serving as a relative possessive pronoun the way it is here.

• You cannot ask Whose branch did this leaf come from? if you are looking for an answer which is a tree not a person or an owl. This is the only situation where whose is forbidden from being used on non-animates like trees — as opposed to men or owls, both well-known for their who affinities.
• However, it's perfectly fine to say That tree over there is the one whose branch lost a leaf. Here it is just a regular old relative pronoun in the possessive case connecting up a subordinate clause, so unlike in the previous example, animacy does not matter.

3. She might have been so tortured when trying to learn the complicated rules for using whom correctly that like a burnt child fearing fire, she's now gun-shy of anything that smells at all whoish.

Yes, it's grammatical.

No, it is not in good style.

No, you cannot be assured that everyone will process it correctly. Just because something is grammatical doesn't mean everyone will process it well: I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve.

The best way to say their clunky phrase is:

...another verb, (one) whose present tense I've already talked about.

The optional one might be useful in speech to make sure the listener realizes this is a descriptive clause not a restrictive one.

Why the person said the clumsy version instead of the simple and clear — and to my mind obvious — alternative I've proposed we cannot know for certain, but we can make some educated guesses:

1. If you had not made the “But in German this is impossible” proviso, I would have said that her first language might be one where the clumsy way is the only way allowed. Not all languages have single words that work just like whose does in English, or even the wer/wen/wem/wes set of German. If so, said hypothetical speaker might have naturally reached for something more like whatever they're used to, no matter how clumsy that might be in English.
2. She might be suffering under the distressingly widespread misunderstanding that whose is restricted to animates the way who and whom are. It isn't, at least not when serving as a relative possessive pronoun the way it is here.

• You cannot use whose as an interrogative pronoun for non-animates. So you cannot ask Whose branch did this leaf come from? if you are looking for an answer which is a tree not a person or an owl. This is the only situation where whose is forbidden from being used on non-animates like trees — as opposed to men or owls, both well-known for their who affinities.
• However, it's perfectly fine to say That tree over there is the one whose branch lost a leaf. Here it is just a regular old relative pronoun in the possessive case connecting up a subordinate clause, so unlike in the previous example, animacy does not matter.

3. She might have been so tortured when trying to learn the complicated rules for using whom correctly that like a burnt child fearing fire, she's now gun-shy of anything that smells at all whoish.

Yes, it's grammatical.

No, it is not in good style.

No, you cannot be assured that everyone will process it correctly. Just because something is grammatical doesn't mean everyone will process it well: I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve.

The best way to say their clunky phrase is:

...another verb, (one) whose present tense I've already talked about.

The optional one might be useful in speech to make sure the listener realizes this is a descriptive clause not a restrictive one.

Why the person said the clumsy version instead of the simple and clear — and to my mind obvious — alternative I've proposed we cannot know for certain, but we can make some educated guesses:

1. If you had not made the “But in German this is impossible” proviso, I would have said that her first language might be one where the clumsy way is the only way allowed. Not all languages have single words that work just like whose does in English, or even the wer/wen/wem/wes set of German. If so, said hypothetical speaker might have naturally reached for something more like whatever they're used to it, no matter how clumsy it is in English.
2. She might be suffering under the distressingly widespread misunderstanding that whose is restricted to animates the way who and whom are. It isn't, at least not when serving as a relative possessive pronoun the way it is here.

• You cannot ask Whose branch did this leaf come from? if you are looking for an answer which is a tree not a person or an owl. This is the only situation where whose is forbidden from being used on non-animates like trees — as opposed to men or owls, both well-known for their who affinities.
• However, it's perfectly fine to say That tree over there is the one whose branch lost a leaf. Here it is just a regular old relative pronoun in the possessive case connecting up a subordinate clause, so unlike in the previous example, animacy does not matter.

3. She might have been so tortured when trying to learn the complicated rules for using whom correctly that like a burnt child fearing fire, she's now gun-shy of anything that smells at all whoish.

Yes, it's grammatical.

No, it is not in good style.

No, you cannot be assured that everyone will process it correctly. Just because something is grammatical doesn't mean everyone will process it well: I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve.

The best way to say their clunky phrase is:

...another verb, (one) whose present tense I've already talked about.

The optional one might be useful in speech to make sure the listener realizes this is a descriptive clause not a restrictive one.

Why the person said the clumsy version instead of the simple and clear — and to my mind obvious — alternative I've proposed we cannot know for certain, but we can make some educated guesses:

1. If you had not made the “But in German this is impossible” proviso, I would have said that her first language might be one where the clumsy way is the only way allowed. Not all languages have single words that work just like whose does in English, or even the wer/wen/wem/wes set of German. If so, said hypothetical speaker might have naturally reached for something more like whatever they're used to, no matter how clumsy that might be in English.
2. She might be suffering under the distressingly widespread misunderstanding that whose is restricted to animates the way who and whom are. It isn't, at least not when serving as a relative possessive pronoun the way it is here.

• You cannot ask Whose branch did this leaf come from? if you are looking for an answer which is a tree not a person or an owl. This is the only situation where whose is forbidden from being used on non-animates like trees — as opposed to men or owls, both well-known for their who affinities.
• However, it's perfectly fine to say That tree over there is the one whose branch lost a leaf. Here it is just a regular old relative pronoun in the possessive case connecting up a subordinate clause, so unlike in the previous example, animacy does not matter.

3. She might have been so tortured when trying to learn the complicated rules for using whom correctly that like a burnt child fearing fire, she's now gun-shy of anything that smells at all whoish.