I'm definitely not a chemist, but I don't think it's glue in the conventional sense. I think it actually changes the chemical state of the rubber into something gooey like modeling clay. The patch itself is already in a similar state (protected by foil). Then when you stick them together, the molecules or polymer chains or whatever is in there meld together, becoming a single continuous piece of rubber (or clay). With regular glue you would still have two distinct pieces of rubber, with a layer of adhesive between them. If there is still solvent in the area, it apparently interferes with the bonding in some way.

It reminds me a little of "chemical welding" cement that is use for bonding some types of plastics, like acrylics and, I think, PVC pipe, except you don't let them dry first.