The advice here is good, better than what you will generally find for this question. The convention seems to be that, for a joint item (combinatorial) with proper nouns (names of people), putting an apostrophe at the end of the combination is best whereas for other cases, both should get an apostrophe. Thus, "Jack and Jill's bucket" but the "writers' and editors' wages". Some suggest that the latter is correct only if the target item (the wages) is actually a multiple/separate form (so the writers have wages and the editors have wages). I disagree, and think this is generally less clear.
Consider "John and Jill's dogs are friendly". The general argument found around the web and in, it seems, many publication guides, is that this will be interpreted as the dogs of John and Jill are friendly. But a strict reading of it says that John is friendly and Jill's dogs are friendly. Indeed, if the latter meaning was what was intended, it would be written the same way (unless the sentence is completely restructured). This weakens the value of the apostrophe in indicating possession.
A different case may help. If I want to say that the teacher was talking to me, and also to John, I would say that the teacher was teaching to John and me. The way to teach kids to get this right (and thus not say 'I') is to take out John and just have it for me. The correct form is now easier to see for kids. The rule here is that the sentence should work if just for "me".
The same logic should be applied to apostrophes. "John's and Jill's dogs" holds true for this approach, but "John and Jill's dogs" doesn't. There is no ambiguity in the former, aside from whether the dogs are co-owned or separate dogs. However, I would argue that conveying this latter information is not the job of the conjunctive structure/use of the apostrophe. That is, the apostrophe should indicate possession. If that leads to ambiguity on whether the target is a singular shared target or separate targets, then that needs to be corrected in some other way. It is unlikely that you would have a problem using the apostrophe this way, though, as context is likely to have already conveyed the nature of the target. Whereas the approach of just putting an apostrophe at the end of the joint pairing (John and Jill) does create ambiguity because there are plenty of cases where context will not make it clear that it is a pair.
I think publication guides lean toward "John and Jill's conclusion" is because they are actually personifying a manuscript. That is, what is often being said in a manuscript is "the conclusion in the manuscript by John and Jill...", and the short-hand becomes the "John and Jill's conclusion" because the sense is that the conclusion belongs to the manuscript (referred to in manuscripts as John and Jill), not to John and Jill the people. That is technically wrong, but the alternative is more wordy and can feel clunky. But it seems to have led to the guides being used as writing bibles and a special case corrupting general use.