Yes I was joking, but it does depend on the circumstances. If unconsious, then they are in control and have to do whatever, no complaint.
I might ask a paramedic not to do so, if they are looking a bit too keen, and there were other viable alternatives. That would involve a quick discussion and my taking a personal risk decision.
e.g. leave the TQ on over the leathers as a contingency until we get to hospital, and better diagnostics/help. Or my ability to move/lift my hips and slide down my trousers.
The risk of an undiagnosed injury is clear, and could be fatal or loss of a limb. However, (my thinking, not any medical training) an external injury will be relatively obvious and probably visible, and therefore treatable, whereas an internal one probably not. Unless my blood pressure was dropping like a stone, which might easily be my spleen.
"Obvious" includes the amount of blood leaking out. A greenstick external break of say thigh bone will either be obvious or leak like a faucet, a tear in the leathers ditto. Whereas skin shear due to friction will leak but not hugely, but probably hurt like hell., and best if the leathers are left on until peeled off in hospital.
Fun considerations when out riding my bike!!
I do intend to get What3Wrods on my phone though, that cpould be a lifesaver (if it can spell better than my typing

)