I just wanted to add that when I taught my son to ride without training wheels, we had to also talk with him about rules and etiquette for bike riding once he learned how to ride. For example, he learned to slow down when riding with other kids, that he shares the sidewalk/bikepath with people who are walking and needs to slow down by them and let them know he is going past them, he needed to learn to stop well before a crosswalk or driveway, wear a helmut, etc.
As far as learning to ride, I agree that they have to be able to touch the ground with both feet. We lowered his seat all the way down event though it seemed to short, but it helped him feel confidant that he would be safe, and we had him ride on the sidewalk next to the grass - we told him that if he lost his balance to either put his feet down or let himself fall onto the grass. In retrospect, I would have invested in knee pads for the first few weeks because he did fall on his knees a lot, even though he was riding his bike beautifully in one day.