1) I am so sorry to correct you but you have exactly opposite! If you ignore the timing and look at the foot work you will see that "the Basic Step" in the Mambo is IDENTICAL to "the Basic Step" of the International Rhumba (including Timing - 2,3,4)...(M) fwd, rk, bk (F) bk, rk, fwd.
If anything, the American Rhumba is based on the American Waltz box step...
2) "How did American Rhumba ever get invented?" Please reference the late 50's and 60's for the origin of the American Rhumba. Songs like "Venus" by Frankie Avelon and "Lonely Teardrops". Very fast, uptempo love songs done to box step rhythms S, Q, Q.
What is most interesting is that the mainstream popularity of dancing to this type of tempo (now known as "American Style Rhumba") was picked up by Disney and Hanna Barbara and you can see cartoon characters including Fred & Wilma Flintstone dancing what we now call "the Rhumba."
3) I know this sounds cruel, but please don't don't come across as an expertt regarding American Style Rhythm when you really don't know what you're talking about!
4) Good dancers CAN "create good hip and body movement at this speeed." It took me about 10 years... :)