I'm certainly not gonna get into what some states do, and do NOT, allow an EMT-Basic to do. That could be a whole thread unto itself. HOWEVER, I think mycrofts point was overlooked a bit. Not only does each state declare what their license levels can provide, but each state's labor regulations declare how wages are to be paid, or not paid. What might be completely legal in one state, may, or may not, be legal to do in another state.
As to trevor's original post. What you described is similar to the way our EMS squad runs. We have several 'paid full timers' that run a 24 on, 48 off shift. They are salaried. Then we have 'paid part timers' who work UP TO 40 hours and are paid by the hour. We also have 'paid on call' members who sign up for whatever shift happens to be open due to either illness, vacation time, jury duty, etc, etc, etc. who are also paid by the hour. Lastly, we have 'volunteers' that run a set 6 or 12 hours per week and they get paid 10.00 per run as a basic, 12.00 as an intermediate, and 15.00 as a paramedic. Also same as you described, no transport, no pay, including DOA's.