Well, the current HCR bill says they can wait, at least according to my reading of it. I understand what you’re saying and I don’t have a practical answer for it. If the rules say that the insurance companies don’t have to pay immediately for a pre-existing health condition (although some won’t make you wait), it means that they only cover new medical problems until the wait period is over, then coverage for the pre-existing condition begins. I would imagine, then, that the cost of treatment is on the patient for that period.
So, if a cancer patient has a slip-and-fall accident, that will be covered; their cancer meds, for example, won’t be covered for 90 days. After the 90 days, the health insurance will cover those cancer meds.
As for auto accidents (which you did not mention specifically, but I’ve seen other folks raise the issue), I know of no health insurance company that will cover injuries from auto accidents. That is covered by auto insurance; either your own or another party’s auto insurance, depending on whether or not you live in a no-fault state. In the case where no involved party has auto insurance, the funds come out of a minimum-coverage state insurance pool. Perhaps this varies in different states, but a health insurance company here is not on the hook to cover injuries from an auto accident.