Yeah, I suppose this question has dragged on a bit too much. There's only 3 options left, so I suppose there's not much mystery left.
The missing #1 AP team to win the title was UCLA in 1995. They had 6 NBA players on that roster: Ed O'Bannon, Tyus Edney, George Zidek, Charles O'Bannon, Toby Bailey, and JR Henderson. Most of the guys flamed out after 2-3 years in the league. UCLA beat Duke on February 26th and they were bumped up to #1 the very next day... and they kept that #1 ranking the rest of the season.
hart got the first half of the previous question correct - so I suppose it's hart's turn.