Chris Hoogstad, JFK/LGA/EWR FA base manager, has indicated the early morning vans to EWR are actually paid for by the crew scheduling department to help alleviate the difficulties with early morning sign-ins at EWR. They belong to neither Flight Service nor Flight and should be on a first come, first serve basis.
A myth that the early morning late night vans are fo Flight Attendants. I got this from Union page.