Side View Mirror

The passenger-side side view mirror on my daughter’s Toyota RAV4 was damaged while she parked at her school last Thursday. Don’t know who did it.

I took it to a auto body shop and their estimate is $290 parts + $52 labor. It’s reasonable considering $350 parts + $168 labor at the dealer.

However, when I searched online, there are side view mirror assemblies at about $50 (they are not made by Toyota but fit the specific model).

Does anyone know how important it is to use genuine parts? Can I request the auto shop to replace with parts that I supply? 

Thanks in advance for your input!