Thos people are idiots, and certainly not physicists. When you stop running, your body does NOT continue on at the same speed, it begins to slow down as soon as you stop accelerating. Secondly, players dive for ground balls because the ball is on the ground. It's not enough to simply reach the ball with your feet, you must actually pick it up with your hand if you wish to make a throw.
Apparently, according to Wikipedia, the good folks at the Discovery Channels' Mythbusters have done an episode on the subject, but I couldn't find it on their website. The Wikipedia entry suggested that Mythbusters determined that sliding is marginally faster, and that the tv show guessed it was because of faster deceleration from sliding. Of course that wouldn't apply for first base, and like I said, I couldn't find a description of the episode. Except on Wikipedia.
There was also on the internet a discussion of a comparison done on ESPN, where tape of runners who typically slid into first was timed against tape of the same runners when they didn't slide. The discussion said that ESPN found sliding faster for those runners, but maybe they were slacking when they didn't slide?
I don't know whether those reports are right or not, but if the difference is infintessimal, it would seem like the greater danger of injury to the runner would argue for not sliding into first. Not that sliding presents any danger of injury to runners. Or diving for ground balls.