The reason I had the stylist put the rubber facing the scalp in the current video that I'm editing is because of this:
I hope you can read this (please click on the photo to make it larger). It comes from one of my booklets on how to do a permanent wave perm. You'll see that it says to "Pull the strand of hair through the rubber-felt with rubber side NEXT to the scalp" and "Open the spacer and place on top of the FELT..."
As evidenced from several of my spacers, felt bits still remained on the rubber part of the spacers. So I am going to theorize that because the clamps get so hot, the rubber, rather than the felt, is placed on the face because the rubber would melt to the spacer, thus ruining the pad completely and the melted rubber would seal the spacer shut, ruining the hair as the hair would have to be cut off from the spacer.
The felt part of the pad would also help to keep the perm solution off the skin as any leaking perm solution would be soaked up by the felt. If the rubber part was on the outside, any perm solution that leaked would slide off the rubber and come into contact with the face, other skin, and cape or clothing.
Like all Hollywood productions, you have to take it with a grain of salt; not everything they do or show is 100% acurate. And they don't need to as they are trying to produce something that is entertaining rather than educational. But if people would rather see the rubber part of the pads on the outside in the next perm machine video that I make, please let me know, and I'll happily do it that way.