The genitive apostrophe marks a phrase, not a word. Consider:
Hamlet is the tale of the Prince of Denmark's tragedy
The tragedy belongs to the prince, not to Denmark, but the apostrophe is covering the whole phrase Prince of Denmark.
He said he didn't know anything about John and Jenna's deaths.
Here it is John and Jenna who had deaths, and again this is perfectly okay.
The suggested alternative would be:
?He said he didn't know anything about John's and Jenna's deaths.
?He said he didn't know anything about John's and Jenna's death.
This is certainly found, particularly in speech rather than writing, and perhaps with local variation (I can imagine hearing it being more likely where I grew up than where I live now). It's also clearly logical (it belongs to each of them separately) but it's the sort of thing that might raise objections. I would expect an editor to put a red pen through it.
He said he didn't know anything about the deaths of John and Jenna.
That certainly avoids the question. In this case I think "… John and Jenna's deaths" is clear enough and reads better and would just use it. In cases where there was more ambiguity such re-wordings can be wise.