In a nutshell , why the door puzzle was a 'non-puzzle', fooling those
thinking themselves clever from a previous situation.
When that puzzle is usually given (ie before Labyrinth) it's given by an OBJECTIVE narrator e.g 'You find 2 doors..'
In Labyrinth , the 'puzzle' is instead given by a SUBJECTIVE thing - one of the doors.
Now, unlike the original form of the puzzle , it has become a non-puzzle because the original door might always lie or sometimes lie or never lie and so might the other door NO MATTER WHAT ONE OF THE DOORS CLAIMED SUPPOSEDLY 'in advance'. It'd still be a non-puzzle even if Tweedledum and Tweedledee were in front of the doors. The character supposedly setting the 'puzzle' would not be an OBJECTIVE narrator .
There can be no 'in advance' with a subjective character in true/false terms, unless an objective narrator lays down the ground rules.
Furthermore , (not that she does but) it's not necessarily a good idea to try to best guess the truth based on the surface character of the doors , e.g from their mannerisms. Particularly since possibly everything in the Labyrinth is an extension of Jareth himself. It's one giant crystal ball.
Your best course of action is to either go through neither door or to open one with far more trepidation than she does. Unless you trust Jareth to bring you to no physical harm no matter what you do, just as a nightmare doesn't truly harm you, aside from psychological worry that may have caused you to have the nightmare in the first place and which is then perpetuated by having had a nightmare.
This accidental, or more likely deliberate (Terry Jones is clever to attack presumption of logic) 'non-puzzle' , in disguise of a classic puzzle, will have made fools of many 'maths people' if only they knew or allowed it.