Does Rover verify pet vaccinations are current or should sitters do that at booking when setting up a meet and greet?

No, Rover does not take any responsibility in that area. From the Terms of Service:

Pet Owners and Service Providers are solely responsible for making decisions that are in the best interests of themselves and their pets. For example, each user of the Rover.com Service is responsible for keeping current his or her own pet’s vaccinations, and we will have no liability for anyone’s failure to vaccinate his or her pet.

It is the sitter's responsibility to as for and check on their client's vaccination records.