What is fundamental to LLM's that make it impossible for them to infer intent?
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?
“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)