Did my 82 year old mother get ripped off?

Can’t speak to the configuration of this particular car, but my Corolla’s water pump pulley is re-used on pump replacement, not part of the water pump ass’y. After the pulley-less new pump is installed on the engine, then the pulley from the old pump is bolted back onto the newly installed pump. This is a bit of a tricky maneuver b/c there’s not much room to work, engine has to be raised just to provide the space there is, so certainly conceivable someone might forget to bolt the pulley back on, or not tighten the bolts. It’s also possible the tensioner failed coincidentally.