This makes little sense, even though it sounds superficially convincing. However, why would a language model assume that the car is at the destination when evaluating the difference between walking or driving? Why not mention that, it it was really assuming it?
What seems to me far, far more likely to be happening here is that the phrase "walk or drive for <short distance>" is too strongly associated in the training data with the "walk" response, and the "car wash" part of the question simply can't flip enough weights to matter in the default response. This is also to be expected given that there are likely extremely few similar questions in the training set, since people just don't ask about what mode of transport is better for arriving at a car wash.
This is a clear case of a language model having language model limitations. Once you add more text in the prompt, you reduce the overall weight of the "walk or drive" part of the question, and the other relevant parts of the phrase get to matter more for the response.