Some RFT are safe to be repaired, some are not, any damage to the tire will compromise the structural integrity of the entire tire.
I believe the manufacturers that are repairable: Michelin ZP tires, Bridgestone RFT tires, Goodyear and Dunlop EMT tires and DSST tires, and BFG runflat tires.
Manufacturers that are not repairable: Pirelli, Yokohama, Kumho, and Continental.
Most places don't want to work on them because they probably don't have a replacement in stock and half the time the liner on the inner sidewalls is completely shredded.
I know Discount Tire Co and Americas Tire Co will repair runflat tires as long as the hole isn't too big, it isn't outside the steel belt reinforced area of the tread, and there isn't any sidewall or shoulder damage. They reference the list above and update that list as the manufacturers do.
In general a plug is just a piece of strung with gooey stuff on it that temporarily slows or stops a leak until that goo dries out. A properly installed patch will actually chemically bond to the liner reinforcing that area (and make it 3-5 times thicker in that area). Both should only be applied to the rigid steel belted area of the tire, since the sidewall and shoulder are designed to flex, damage to that area can get worse as the tire is driven on.
Also, the slime stuff is not intended to be left in the tire indefinitely. It is combined with a plug and compressor in lieu of a spare, and may damage the liner of the tire. It can get you somewhere safely, and like above could take you thousands of miles, but it isn't intended to.