a shop is not going to have to provide any sort of warranty for parts brought in by the customer. What a shop loses in profit on parts they gain in loss of liability. Sure if there is a direct connection to failed labor there may be an issue.

There is no cost to the shop for using a customers parts. It's inventory you don't have to keep, parts you don't have to buy via your accounts and alot less paperwork all round.

I do tons of oil changes on vehicles coming up from the states going to Alaska. A small number of them bring their own filter/oil ... I'm more then happy to have them in an out of my bay and i'm 20-30 richer.

Raising labor rate for customers not buying parts off of you = greed

I do agree with charging more labor if the customer wants to help