I've had mine in for basic scheduled service once, now. The experience was excellent. Basically, I called them up and scheduled a convenient pickup and dropoff time at my home. I had to choose a day a few days into the future, just due to availability, as I expected. I also asked if I could have a G80 as a loaner, if they had one available to lend, just to try it out for the day. They said yes, on the condition that one was available.
The day arrives, and I get a text notifying me my loaner was on the way and it arrived at the specified time. It was indeed a G80, as requested. We swap keys (and a bit of paperwork) and away we go. The dropoff went the same, with a text notification and arrival at the expected time.
My car was returned serviced, washed and ready to rock and roll. As for where it went, my understanding is that even if it is taken to a Hyundai dealership for service, only Genesis techs will be allowed to work on it. Of course, I suppose I'll have to take their word for it, but since I never went anywhere near the service department, it doesn't really matter in the end if it was on a lift next to a clapped out 1987 Excel.