There's nothing inherently wrong with a single-member LLC. The only issue with it is it's a relatively new entity and the body of legal precedents is not large, so it's hard to predict how a court would rule in any particular case.

Instead, you could use an S-corporation with the same result, but much better legal visibility.

The issue is, however, that you're now operating your own rental company. You'd need to capitalize it, buy commercial insurance, purchase various licenses, etc. This is probably not what clients of RelayRides had in mind.