It's not logic; logic has to do with meaning. It's syntax, which has to do with sentence grammaticality (no matter what the sentence means). In the following examples, parentheses mark optional material, and asterisk marks ungrammaticality (asterisk before a parenthesis means deleting the material inside is forbidden, so (2) is ungrammatical without who or that).
- Who’s the girl (who is) dancing over there?
(grammatical with or without who is)
- Who's the girl *(who/that) danced with my husband?
(ungrammatical without relative pronoun who or that)
- The people (who were) invited to the party had a great time
(grammatical with or without who were)
The reason why (1) and (3) are grammatical but (2) isn't is obvious in the parentheses above. (1) and (3) both delete a string consisting of a relative pronoun (who or that in this case) plus a form of be that agrees with that pronoun (is and were in this case). That's the form that the well-known English syntactic rule of Whiz-Deletion requires.
And it really doesn't have anything to do with which kind of participle is used. Note that past participles are OK, provided they use auxiliary be, like the Passive construction:
- Who was the girl (who/that was) arrested for dancing in the street?
(2), on the other hand, only deletes the relative pronoun, and not any auxiliary form of be. There is no syntactic rule that allows such deletions. So it's ungrammatical because it doesn't follow the grammatical rule, while (1) and (3) are grammatical because they do follow the grammatical rule. There are a lot of grammatical rules like Whiz-Deletion, and they produce ungrammatical sentences when they're not applied correctly.