I ended up buying my own tire mounter from a shop that was closing down and it took me a while to learn what I was doing. However, I just mounted four new OEM tires on four new rims and these PS4S are way easier to mount than the run flats on the C7. I have no idea why it would take them 3 hours to mount them.
A common problem, even with the touchless machines, is that folks don't hold the tire down into the drop center as it's fed around. In that case, the tire can actually pull the mounting arm down to the wheel or can rip the bead - I've done both mounting stock tires for the C7. Based on your picture it looks like that's what happened. The arm that feeds the tire down over the lip also has a replaceable plastic piece that will wear and crack off, so if that's missing you're going to get metal to rim contact which will actually gouge the metal.