This is due to a slipped timing belt, likely happened because they didn’t test or replace the tensioner, and should not have happened. They are IMHO responsible UNLESS the suggested changing the tensioner too and you “passed” to save money.
Their denial is based on their assumption that the only possible reason the camshaft could be out of time were if it were that way when they did the work. The assumption is invalid. Or, much more likely, they know they screwed up and are avoiding financial responsibility.