The problem inherently indicated that the labels were untrustworthy. It was impossible for them both to be true, because one explicitly stated that only one was true. I see no reason to trust the red label more than the green label, so at that point, it should be clear that neither can be trusted.
It's interesting in that people seem to trust meta-statements like the red label's more than they trust basic statements like the green label's.
Only when such statements are made by the narrator, not the puzzle artifacts themselves. The whole point of these sorts of puzzles is that the labels can't all be relied upon, yet some people think the red label can be, for some reason.
The problem is that mjd himself, when discussing "Why don't all logic puzzles fall afoul of this problem", says that the statement
> Portia explained to the suitor that of the three statements, at most one was true.
in a Gardner puzzle is evidence enough that we may trust that "of the three statements, at most one was true". Here, Portia is a character in the puzzle; why should we trust her any more than we should labels on boxes or (in the set-up of the puzzle) statements on caskets? If we have to distrust everything about the problem, then it seems to me that it runs into exactly the problem shultays (https://news.ycombinator.com/item?id=9837381) mentions.
It's interesting in that people seem to trust meta-statements like the red label's more than they trust basic statements like the green label's.