My point was that sliding across the floor is not a travel. The NFHS case book addresses a player sliding on either back or stomach after diving for a loose ball (4.44.5 Situation B). After gaining control of the ball and sliding across the floor, that player "may pass, shoot, start a dribble or call a time-out." Neither the NCAA rule book nor case book addresses sliding (your citation e. above is not from the NCAA basketball rules), but the NCAA's definition of a travel is almost identical to that of the NFHS. A player can slide as far as he wants across the floor without violating the traveling rule.
Your reference to 4-70.6 may be valid. I wasn't really addressing whether his fall to the floor was a travel. The officials would probably argue, though, that the Vandy player did not violate this rule since he was not holding the ball when he went to the ground but was maintaining a dribble as he fell.