Sorry to not answer your question about removing the fuel door. Is yours round or more square shaped?
The paint code from the VIN tag will give the shop the formula to mix the same color. But it is still different paint. It you took two of the same cars, same color with different production dates and swapped body parts (a fender or a door) there is a good chance that a visible difference in the color tint would exist.
It is not a bad idea to after mixing the paint to spray a test panel and match it to the existing paint on the vehicle. The paint shop is just trying to insure the customer gets a good product that they will be satisfied with. To advise someone not to comply with the shops request it really not being very helpful.