Most shops do not work with aftermarket or customer supplied parts because then they are responsible for making them work. If a tab is bent or a clip broken, they have to make it acceptable for you to go through it with a fine tooth comb.

My close friend runs a bodyshop and I hear about this stuff everyday. There is just no way to know that you are going to bring in good parts, especially if you do not know exactly what to look for since you do not do bodywork everyday. It may seem like a simple job, but there is TONS of labor involved and it can easily cost more to massage a used part back to life than simply buying new, in some cases. In other cases you could use all used parts and it be totally fine, or aftermarket and it is better than fine, but unless they know you and trust you and your skill to examine parts, they are probably going to insist on getting their own. You are not going to see the ever so slight bend on a fender that is not on a car, but making that fit could take hours, if it is even possible. If you were that good, you would have already sourced the parts, prepped everything, assembled and taken it just for paint.

If you were having surgery, would you insist on bringing or sterilizing your own instruments? To a good body guy, he is doing a complex surgery on your car, just keep that in mind.

Best of luck with the repairs, hopefully you can find the right shop. You may want to ask user Zahanma, if memory serves he is from Houston and may be able to help find a shop.