“We see emotion.”—We do not see facial contortions and make inferences from them … to joy, grief, boredom. We describe a face immediately as sad, radiant, bored, even when we are unable to give any other description of the features. (Wittgenstein 1967, §225)
All the limitations you are describing with respect to LLM's are the same as humans. Would a human tripping up on an ambiguously worded question mean they are always just faking their thinking?