Puzzles are definitely odd birds. I myself have gotten into a literal screaming match try to push my belief that they never should be used in interviews. The bulk of that was an interviewer said the interviewee was "clearly confused when they were asked a puzzle" yet refused to agree that may evidence the presentation of the puzzle may in fact be confusing (and not measuring anything).

I can't speak for Winkler, but both he and Jaynes implicitly separate the reading of the puzzle from the work. Winkler start his book with a few awful "reading trick ones", but in the explanations gives a few reading directions to try and avoid that going forward. I happen to know he meant "on a Tuesday." But a correct solution to a different read would be a correct solution even if it doesn't match the book text. I don't think he was trying to set a text trap, it is just hard to be clear, concise, and unambiguous at the same time. (Even "on a Tuesday" isn't completely clear if it means "all I am telling you was the day of week was Tuesday" versus "it was a very specific Tuesday, that I am not telling.")

The value of puzzles in interviewing is never about reaching the solution. It is about seeing how candidates deal with tricky situations that stretch them a bit, because that happens all the time on the job. It should almost always be done interactively, so you can see what clarifications and extra information they ask for, when and how they give up, and if they're dumb enough to say HR violations out loud (it does happen).

This does require a rather skilled interviewer, so the benefits may well not be worth it. But it can be very interesting information to have.