It's more than just shimmy.
Rotors have a minimum thickness spec for machining and service limit, below which they should be discarded. A shop that willingly goes below this is opening themselves up to all sorts of liability if something should go wrong. A lot of hard brake users will develop tiny surface cracks in the rotor (squarebody fords...Jesus Christ!), and its not hard to imagine this growing (as cracks are want to do) completely through. I would imagine the thinner the material gets, the more likely this could happen...though I've never seen it myself. And as @Mopower58 said, it seems like they warp easier as they get thinner.
I do not generally turn rotors on my own cars unless they are minimum or shimmy anyway. The reason they get turned otherwise is to provide a new surface for the fresh pads. Not doing this can sometimes cause weird sounds an pedal feedback. I know this (hence not turning my own)...and It goes away quickly...but in this day and age, everybody feels like the average shop is cheating them thanks to "undercover videos" and such, so the likelihood hood of a customer returning minutes later after that new brake job and complaining is very high.
This is also the reason i always do a test drive similar to what @Neohio was talking about to seat/heat the pads. New pads on new rotors don't have the same feel and power as the ones they drove in on, and people don't like paying money to jump in the car and be greeted with less braking than before. Again, as they seat in they come good, but the average customer these days can't even check the oil, much less know the ins and outs of braking. Better to head off trouble before it gets started.
Shops and auto parts stores will sometimes throw in a "rotor turning" for your new rotors. The legitimate reason for this is that sometimes new rotors come out of the box warped...or so I'm told. I've never has this happen, so for me its just a waste of rotor.
I've always been told that euro cars (IE-BMW, etc.) are designed to have the rotors replaced at every pad replacement, so certainly, a mfg can choose how durable a rotor material is. My experience with them seems to support that euro rotors typically have large lips on them at pad changes (meaning they have worn down significantly).
Any quality rotor like Raybestos or Wagner will do fine. Just avoid the cheap chinese junk at the bottom of the price range.