I had some work done on a device at one of these independent Apple-certified repair locations. There's a sign in the store telling the customers that they may be contacted by Apple to ask how their experience was.

It's a way for Apple to ensure that the shops flying its flag are quality operations. I'm OK with that. I specifically chose that store because of its relationship with Apple.

remove battery / screen from client device... etc...

That sounds like an extreme case. My repair took three days, and only because the shop was out of the battery I needed, and had to order a new one from Apple. The store said the work is usually done the same day.