This is correct, but based on specific assumptions. If the host flipped a coin and selected a door and 1/Nth of the time it had the car then you switching would not change your odds.

Similarly, an adversarial host who sometimes opens a door and sometimes just shows you your choice can similarly mess with the odds.

It’s really due to the host both being forced to show a door and knowing which door to choose that you gain from leveraging that knowledge.