EMT's should not be removing your helmet after an impact! I used to have a sticker on my helmets indicating NOT to remove my helmet before I am being treated in either the trama unit or by a doctor.
How would you do CPR (the breath part) without removing the helmet? If you ain't breathing, you won't last long. ;-)
I was in that situation where a fellow rider went down hard and he was not breathing. We carefully removed the full face helmet
as best we could (cradling the neck and spine, etc.) to prepare for CPR (I am trained in it).
In his case, the chin bar had pushed up and jammed his mouth shut and his nose was blocked -closing all airways.
(He hit pretty hard off road - destroyed the front end of a ST1100 completely).
Once we got the helmet off, we heard him take a deep gasp and he regained consciousness.
He recovered fine after he was airlifted from a small local hospital (we were in the middle of nowhere - far from any trauma center).