Vanilla Ice is the first rapper in history to have a No. 1 hit (''Ice Ice Baby'') and probably the first big rapper to be caught with falsified street credentials. Perhaps to establish the credibility that rappers especially white ones need, Ice claimed to have gone to the same Miami high school as 2 Live Crew's Luther Campbell. He also said he had grown up in the ghetto, that his mother taught music at a university in Miami, and that he had been a three-time national motocross champion for Team Honda. It turns out different. Ice, 22, whose real name is Robert Van Winkle, grew up and went to high schoolin an affluent Dallas suburb, and Honda's never heard of him. After finding no evidence that his mother taught music in Miami, a Dallas Morning News reporter asked him what his mom really did. ''None of your (expletive) business,'' Ice/Van Winkle replied. Moreover, he didn't credit his hit's bass line, sampled from the 1981 Queen-David Bowie collaboration, ''Under Pressure.''