It's incredibly simple to remove humans from those decisions. Just have the self-driving code refuse to engage until the issue is resolved.
Calling an ambulance is currently the recommended thing to do in severe medical emergencies anyway.
For other concerns about availability, adjust maintenance inspections and routines as necessary. For example, if you live somewhere there is no ambulance service and someone is of uncertain health, maybe inspect the tires every day (this sounds tedious but look at the alternative you are proposing, having a tire blow out while delivering dying Grandma to the ER).
I also expect that automatic systems will greatly improve the level of maintenance of vehicles (for example, mandatory tire pressure monitoring already does...).
This is a flawed comparison because failing to update your software or keep your tires inflated or clean off your sensors would also be human decisions that could lead to adverse outcomes with self-driving cars.
Non-driving-operation decisions like that are applicable to both regular and self-driving cars.