Prince is a brilliant musician and like many highly-talented people he is slightly peculiar. His performance clearly wasn't lipsynched as he inserted "topical" comments about the rain that couldn't have been recorded and rehearsed so quickly. I wish he had sufficient time to spend another minute or two on the great "All Along The Watchtower" song by Jimi Hendrix that he covered as a portion of the medley. His guitarwork sounded great.
~ Blue Jays ~
FYI - All along the watchtower was written by Bob Dylan.
You are right about the lack of lip synching, when Prince pushed over his mike stand, you heard the pop when it hit the ground. His guitar work also appeared real.