The usual distance bounding protocols only need a nano-second accurate timer on one device called the verifier. For example https://www.usenix.org/legacy/event/sec10/tech/full_papers/R...

Cool trick in that one, the Prover(i.e. the key fob) does the distance measuring part of the challenge response protocol using analog only components. This means its response time is <1 nano second.

So you can do it with only the car having a good timer.