Should I demand my car be fixed or take it somewhere else?

I agree that there must have been some preexisting condition that caused the tire to burst. The static burst pressure of a healthy tire is well over 100 psi, and shops generally run their compressed air systems around 95 psi. However, it’s usually prudent to inspect tires before adding air to them and note any defects to the customer before blowing them apart. A quick inspection probably would have turned up a bubble in the sidewall which could have been caused by running the tire pressure too low and/or striking a curb or road hazard.

I would bet that if the tire had a bubble in the sidewall or the tread was worn down to cord showing, that a bit of over inflation would easily get it to pop.

If the original poster would mention if the tire was severely worn, or had a bubble in the sidewall, then we could put this part of the issue to rest.

Since its a California car, and the OP seems to be fairly low key when it comes to anything with the car and maintenance, I would bet the tire was in shoddy shape, and the shop guy decided to take a slightly dangerous tire off the road.

Owning a '98 Escort, and not having enough money to worry about a $250 repair makes me think the car is in pretty bad shape overall.

BC.