And how would you know? I've had chains and rings wear quite quickly on lower-end MTBs around the one-year mark. It depends on how often the bike was ridden. If the OP is a daily commuter in gritty conditions, and doesn't lube often or even infrequently, I can see it happening.

And just to be clear, he has the documentation to say that area of the bike was checked, and that the shop has admitted the chain slips on the big chainring. Seems to me that shop liability is as clear as a bell here.

Tough audience.