If the car really did jump time, it's highly unlikely that the belt failed. The usual culprits are the cogged idler pulley, or the hydraulic tensioner. Those are what I see fail on all of the timing failures that come through the shop where I work (yes with bent valves)
It is also unlikely that either of those failed at 88k. We usually see the idlers get noisy around 110K and bearings fail at 130K or more. Tensioners don't usually fail until 150K+ or if they've been re-installed and pushed back in improperly. The other cause can be debris going through the belt and gears, but that only happens when the covers are either broken or removed.
Since the shop is telling you this, ask them to show you what they found. In order to diagnose that they would have to at least taken the side covers off to see the belt slack. You have to remove a lot more than that to see the rest of the belt, pulleys etc. If the timing covers are still on, find another shop.
Now, if it really did jump time and bend valves, you will be looking at $2500 and up to repair by a shop. If you have some mechanical gumption or friends with skill, you could save tons by doing the engine pull and disassembly yourself. A good machine shop should be able to rebuild those heads for $5-600. Figure a couple hundred more for gaskets and beer. Reassemble and install. Keep us posted what you learn from the shop. I hope it's not bad for you.