You and Alicorn are confusing denotation and connotation here. "Edible" simply means "able to be eaten"; it is used instead of "eatable", because the latter is for some reason not considered a "standard" or "legitimate" word. As such, it possesses exactly the same semantics as "eatable" would; in fact, a sufficiently supercilious English teacher will correct you to "edible" if you say "eatable". (Similarly "legible" instead of "readable", although "readable" seems to be increasingly accepted these days.)

Yes, it's true that people only usually apply the word to a more restricted subset of things than those which won't kill the eater; but such a behavioral tendency should not be confused with the actual semantics of the word.

The sense of the quote is exactly the same as if it had been:

All mushrooms can be eaten. But some of them can be eaten only once.

In this case, it would hardly be legitimate to complain that "can be eaten" means "safe to be eaten". The fact is that the phrase is ambiguous, and the quote is a play on that ambiguity. Likewise in its original form, with "edible".

It just seems like a...definitional argument that is primarily about status.

You've just provided a reasonable first-approximation analysis of wit!