I would assume to lubricate the tire/runflat contact area during a flat, I have been told the RF "grease" is water soluble and would again assume it was designed to be compatible with the tire materials, what happens in the "field" is anybody's guess.
None of that changes the fact that putting "axle grease" in a tire is a bad idea. just like using a solvent like ether to "inflate" a tire is a bad idea, much of the solvent is not burned and remains in the tire to attack the rubber over time.
If you go to a real tire shop you will not find them running axle grease around the bead of a tire, they will be using Murphy's tire soap which is derived from vegetable oil, been there done that!!