In order to have some kind of resolution to this question, which doesn't seem likely to ever get a definitive answer (maybe because it doesn't have one? Wow, that aged like milk! See the accepted answer) I will post the following as a Community Wiki. It isn't really an answer, mostly speculation and discussion, but does provide more background on the question and links to some interesting discussions both on Stack Exchange and elsewhere. Other contributions to this post are welcome!
TL/DR: Don't read the wall of text, just click the links :D
Others have already addressed the main points better than I could.
More Background Info:
In languages which have deponent verbs, there is also often a related concept called the 'middle voice.' The meaning of the middle voice is exactly what it sounds like: something in between active and passive. The subject performing the action could be thought of as also being the object of the action. The middle voice is another feature English isn't normally said to have (although see this discussion), but there are words in English which carry that same kind of 'reflexive' meaning. I would say that 'arrive' fits in that category, and so does 'return' when used as a synonym for 'arrive' and not transitively. These describe actions which affect the entity performing the action.
Since deponents can come from the middle voice as well as from the passive*, that might be a better explanation for the example sentences in my original question. This occurred to me while writing the question, but I didn't want to confuse the issue by adding any superfluous details. Bringing up the additional topic of the middle voice didn't seem strictly necessary to understand the question.
I also didn't want to clutter up the question with detailed analysis of specific syntactic forms, which is why I went with simply "past tense" instead of more precisely specifying the usage of 'arrived' and 'returned'. This omission generated a long discussion in the comments about whether the usage of 'past tense' there was incorrect, and even whether non-finite verb forms can be said to have the attribute of 'tense' at all, or whether it's correct to say the form is "used as an adjective" (the most mainstream answer to both questions is yes, although some alternative models of grammar disagree. I'm not criticizing the alternative models - I'm sure they exist because they must explain some things in a way that the standard textbook model can't - but adopting one of these alternatives shouldn't be necessary or relevant to understanding the question here).
Usage Clarification (see comments under the question, and also see @James K's answer):
To clear up any confusion I may have caused with oversimplification and/or poor wording choices in the original question, I will include some of the details of that discussion here. The forms 'arrived' and 'returned' in my example sentences are the past** participle (used as an adjective). This form, both in its adjective form (cf. observed) and in the corresponding perfect (as opposed to just 'past') construction (e.g. having been observed), generally conveys a passive, not an active meaning. That is what makes the usage of 'arrived' and 'returned' special here: while 'observed' just on its own conveys the same meaning as 'having been observed', 'arrived'/'returned' convey the same meaning as 'having arrived/returned'. This is true for very few other words, which seems to put these in a special class.
**Why specify past at all? That was intended to contrast ‘arrived’ / ‘observed’ with the equivalent forms in the present tense - ‘arriving’ and ‘observing.’ This is relevant because the present participle is active in meaning instead of passive - nothing makes ‘arriving’ special in comparison with ‘observing’ - the ‘deponent’ distinction wouldn’t exist with this form and the question would be meaningless. So, ‘tense’ is relevant only in as far as it is the determining factor for ‘voice’ within a given construction. I could not come up with any other forms of the words ‘arrive’ and ‘return’ (finite or otherwise) that would have an active meaning where the form would generally indicate passive.
In the ELU discussion I linked to below, some comments bring up the point that a lot of the words which can have an active perfect sense with the past participle happen to be intransitive. But, that is not the case with 'return' - 'return' can be transitive! This is why I believe the concept of middle voice might be relevant here: although 'return' is transitive, it isn't being used transitively in the example.
Why I don't consider the question to be resolved:
None of the above definitively answers WHY it's OK to use a form in English which is morphologically passive in a way that conveys an active (or even 'middle voice') meaning. There is a discussion on the ELU site which @MarcInManhattan found, which my question is a near duplicate of, but that question focuses on the requirement of having an adverb before the word 'arrived' and not on the distinction between active and passive.
My question was asking about why the 'passive form/active meaning' construction is valid for this small subset of words like 'arrive' in the first place (I'm fully confident that it is, in fact, valid), and whether there is a technical term or designation for the phenomenon, or for the category of words which it applies to.
Thanks again to @James K, @BillJ, @Lambie, and @MarcInManhattan for their contributions to this discussion!
*Unfortunately, you have to take the linked Wikipedia article with a grain of salt, as the second sentence contradicts the rest of the article. It is not true that deponent verbs "have no active forms" (emphasis added): compare sequens from sequor, sequi, secutus sum. However, this wouldn’t be on topic for the ELL site.
