Only people with formal training in logic, or those who work with formal definitions of logic, have trouble with this aspect of the puzzles.
Trying to return to your more naive understanding of logic not only helps understand the intent of the puzzle, it also makes the puzzle more fun.
I'm genuinely perplexed by this, how is the puzzle even a puzzle if you don't judge it by formal logic?
> it also makes the puzzle more fun.
No; it makes the puzzle illogical and thus about as much fun, for those who prefer logical outcomes, as discussing religion or politics.