To say that Rupp didn't integrate UK basketball is ridiculous. And it's not misrepresenting history to say so. Sorry if you want to say Tom Payne was a 'no show'. He was indeed UK's first black varsity player. (BTW, trivia, who was UK 1st black JV player ?)
Now granted because Payne left early for the pros and there were no others on the 1971-72 freshman team, Hall basically had to start over again. Of course this wasn't anything new since Hall had been Rupp's lead recruiter for a number of years anyway.
As to the issues and resistance that Hall faced in integrating his squad, one can assume that Rupp had it even harder, considering that 1.) by the time Hall was doing it the second time around the rest of the SEC was also integrating and 2.) Hall didn't have the same stigma in the black community that Rupp had.
I believe I've seen Jack Givens comment that he likely would not have attended UK if Rupp was coach, mainly due to pressure from the black community, even though Givens said that he personally had good interactions with Rupp.
I know about Payne and yes you can make the case that the first black player at Kentucky was Tom Payne a player who played for Rupp. I am an avid defender of Rupp against those who claim he was a racist. That claim is bunk. For me however saying that the presence of Tom Payne integrated Kentucky basketball is like saying Ada Lois Sipuel integrated American education in 1948. She may have been the first black in an all white school but she did not integrate education.
I do not belittle Rupp or accept the claims of those that cast pejorative aspersions towards him. I do think saying Kentucky was a integrated program because one black player played one season is a technicality, the first black but hardly an accepted or normal player at Kentucky. The road of integration and the complete task of integration was indeed a systemic effort made by Coach Hall and his integrated staff. You do not hear this term anymore but I remember the term that many racists in Kentucky as well as many other places used, "he's our token ******" so I don't fully accept you premise that Rupp's team was integrated and I doubt Tom Payne would either. Nor do I think in any sense the idea the supreme court had started us on the path towards.
Yes Rupp played the first black player at Kentucky but it was Hall even if only by timing and opportunity that made multiple black coaches and players playing on the court at the same time and feel accepted and safe at Kentucky.