That's not evidence that the model is assuming anything, and this is not a brainteaser. A brainteaser would be exactly the opposite, a question about walking or driving somewhere where the answer is that the car is already there, or maybe different car identities (e.g. "my car was already at the car wash, I was asking about driving another car to go there and wash it!").

If the LLM were really basing its answer on a model of the world where the car is already at the car wash, and you asked it about walking or driving there, it would have to answer that there is no option, you have to walk there since you don't have a car at your origin point.

It might assume that more than one car exists in the world.