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It seems like common sense you'd never strap people down like that.  Not an EMT, I just think instinctually that's not what a reasonable person would do.
It is a clearly stated rule in EMS that no patient is to be restrained in thr prone position and it has been so for a decade. Presumably this is because enough folks died just like this.
They used to "sandwich" combative patients between 2 backboard until that also was a no-no.