I'm not a trainer, but I'll try to get this explanation as nearly right as I can. By pointing your toes, you are keeping the calf muscles that work the Achilles tendon, tight. Tight muscles are more suseptible to overuse injuries, and in this case the tendon is the weakest link in the system. The same thing happens if your saddle is too high and you have to point your toes to reach the bottom of the stroke. If you ride this way, you will be causing your tendon to get stiff, and possibly shortened, instead of long and limber. If you've been told that stretching is good, well, this is the opposite of stretching. A minor inflammation can go away in a few days, small tears can take months to heal. One friend of mine was on crutches for three months. Complete disconnections (rare for cyclists,) require surgery, and actually heal faster than smaller tears, although the repaired connection will never be as strong.
As far as looking at pics of Lance and other pros, most of them ride with their toes a little lower than their heels. This is the natural position of the foot, which I suppose you could define as the position from which effort is required to point the toes further up or down.