OK, I just read the general terms and conditions of Sixt and Europcar (hey, don't laugh!), they don't explicitly forbid using their cars on the 'ring, nor do they forbid taking their cars on "one way tollroads" (which the 'ring is). They forbid participation in motorsports events (which Touristenfahrten aren't) and you have to treat your car "gentle and professional" (that is the paragraph that would get you if you hoon around on the 'ring and/or crash there).
In the general terms and conditions for driving on the 'ring are only cars with transfer plates, short term plates and interchangeable licence plates for oldtimers ("07-plates") not allowed (cars on "H"-plates are however), but rental cars not explicitly forbidden. If there is a sign at the entrance it's something else, but I think that's just their insurance if something happens like "there is a huge sign, you didn't follow it, that's your problem".