I understand your frustration, medical help should have been provided before any questioning. Actually it is not the job of the EMT to question you, if they feel that foul play was involved, they should have reported it to local LEO's.
What is the extent of your medical training? That is the deciding factor on who's scene it is.
Example. If we as LEO's get dispatched to an vehicle accident with injuries, once EMT's arrive, it is no longer our scene. Until the medic's leave.
A couple years ago we drive by an accident, we stop and find the driver hurt pretty bad. We call it in to get help. Then a guy in a truck stops in the road an hops out, we were about to grab him when he tells us he is a medic, he grabs his bag and starts giving first aid to the guy until the ambulance arrives.
We found out that since that was not a criminal investigation, he was in charge until someone with more training than him got there, which is the paramedic that responded. Also that if we would have kept him away from the injured driver, we could be charged