There's truth to that, however it's important understand that the point of the statement is maintaining a balance of speed and accuracy that is appropriate to the circumstances of the situation.At least one well-known instructor will tell you that if your shots can be covered by your hand, you are shooting too slowly. I agree with that.
A lot of people hear a comment like the one quoted above and get the idea that there's no benefit to being able to produce hand-sized groups at 3 yards and so they're satisfied with groups at that distance that can't be covered with a dinner plate. If they are ever required to shoot at longer distances, they may not be able to score solid hits.
For example, a person who can shoot properly sized self-defense groups at 25 yards would need to have the ability to shoot one hole groups at 3 yards.
In a self-defense situation, one wants to be able to rely on a skill level that automatically assesses the range and selects a rate of fire that is appropriate to the distance involved. It's just as counter-productive to shoot very slowly at 3 yards--making solid hits but giving the attacker the opportunity to fire multiple shots to every one of yours--as it is to blast away at a high rate of fire at 25 yards and never connect.