Why shouldn't they, give them something to do. In my county all the hospitals and surgeries are near deserted (admittedly there has been a low incidence of Covid).
Surely it be down to the medical staff at their club. As they'll have being forced to rush back to work as well. The money grabbing but-wipes from TV, the prem league should foot the bill for family and friends of any said player as well if going privately IMO.
I think that most treatments for P.L. players, those requiring expensive surgery for example, are carried out by private specialists. Paid for by the clubs and not the tax payer. You may also want to consider that the players pay huge amounts of tax. Tax that is used to, you're ahead here again aren't you, yep fund the enaichess. They probably contribute far more to the system than they will ever have the need to access themselves. Meanwhile back in the real world.
I for one seriously miss live football, tv or otherwise but willing to wait until its more safe and not rushed back... precations are obvious but not a guarentee of safety.
// So what happens in the scenario were a player requires hospital treatment?//
they do what they always have done
go into an NHS facility and get treatment ....
Private Hospitals do have A+Es etc - they are not that good
you need a place where the doctors ( whether or not they look as tho they have just left skool) have seen a lot of eveything
when neighbour went in ( non playing ) I said to the sudanese junior - this isnt TB is it? ( meaning he had seen a lot - everywhere) and he replied in Arabic - yes I thought you had said good morning doctor how are you in arabic [but then this is a grimy wet city in the north and I thought I must be dreaming)
the answer was no of course