Pictures in UK media of the nursing home tragedy suggest that some patients had been moved to the outside air, which was probably a bit cooler than indoors without air conditioning.

In hot and humid places like Florida, such facilities really ought to have generators able to supply air conditioning.

Media reports are seldom accurate about anything technical, but reading between the lines, I suspect that the nursing home had no utility service for some days, as would be expected in the aftermath of a major hurricane.
It seems that a generator WAS available but not for air conditioning.
It might of course be that power WAS available but that the air conditioning was damaged by the storm. A tree landing on an external chiller or condensing unit would do it.