I think the shop that did the belt replacement should acknowledge their error and fix your car for nothing. But it sounds like they’ve gone into CYA mode. That’s a shame. You’ll need the information from the receipt to see what parts were replaced and what parts were not.
You’re going to have to try to find out exactly what part failed and allowed the valve timing to go off. Something either broke, came loose, or failed in some other way, and unless you find out what that was you’re going to have a hard time getting this repaired for nothing.
I also wonder why only one side of the engine was affected. But again, we don’t know what broke, slipped, came loose, or otherwise caused the failure. Without that knowledge we’re really shooting in the dark.
Here’s what I do know: When they pulled everything apart they should have been able to determine what went wrong. You have to get them to explain it to you, and then explain it to us.
Saying it wasn’t their fault is not enough. They have to prove it, and the only way they can do that is to explain exactly what happened.
Good luck.