The story of the cupping causing a failure in the rear is BS. Unfortunately as you know now, the vibration was the tire separating. Had you stopped and inspected you might have caught it before it popped. But truthfully being an inner tire it's also very probable you would not have seen it even if you did stop to look.
As to the brakes, yeah the shop is not at fault on this one. But take heart, it might just be glazing on the rotors. 20 years ago I would never recommend the following and instead want straight to turning (machining) the front rotors, but experience has taught me otherwise.
Ask the shop if they will pull each rotor and use some sandpaper or a 3m buffer wheel to knock the glazing off the front and back of the rotors then reassemble.
If you are mechanically inclined you can do it yourself.
- Wait for the brakes to cool
- Remove one front wheel at a time with the coach on a suitable safety stand
- Take some 150 or 220 grit sand paper and hand sand diagonally across the rotor in two different directions
- Sand until you have knocked all the shiny off
- Next sand the inside of the rotor (you might have to remove the caliper to access this side)
- Reassemble everything, torque to specs and test drive.