Not to rain on your parade, but if you call BMW NA they will tell you to run Mobil 1 5w-30 oil in your engine, when it meets none of BMW's required specs (the correct grade is 0w-40 which bears BMW LL-01 approval), but BMW NA just hasn't updated their information in the past 10 years.
I'm am guessing the rep is confused as to Dexron VI and Toyota T-IV, which are in-compatable. The party that sets the standard and Licenses the Dexron name (General Motors) states unequivocally that Dexron VI is fully backwards compatible with all prior Dexron standards, and has specifically stopped licensing oil under the former standard. This is no different than when the API comes out with a newer standard (now SM), all older standards are included in the newer standard.
Ironically, you are arguing about the use of Dexron III, while the manual states to use Dexron II. Why is III fine but not VI?
Toyota has used 3 different automatic transmission fluids in the past 15 years, Dexron, T-IV, and now WS (World Standard). None should be used in place of the other, but the most current version of Dexron can be used in place of any earlier version.