Doberluv, I actually have the opposite opinion.
In the VERY beginning, while still on leash, dogs should be prevented from moving. However, once I can move away from the dog to the end of the leash and the dog will stay, even if briefly, I never worry if they move.
If they move and get put back, they are learning. This is why we proof stays with distractions. The fact that the dog moved only means he needs a better understanding of the exercise.
What you may be trying to communicate is that dogs, once distracted and put back a few times ( I would say 2 distractions to get the dog to move, and put him back) and then you should slightly minimize the distraction so that the dog can be successful. Then release, lots of praise, woo hoo, great dog.
I teach the stay in the beginning on leash of course. I start early, as soon as the puppy has a reliable sit. I sit the puppy in heel position. I pull the leash up snug, but not tight, straight up above the puppy's head. Then (and this takes practice) I switch hands to hold the leash with my right hand. This is because the STAY signal needs to be given with the left hand. (The reason for this has to do with Utility exercises, the moving stand, etc. where the stand/stay signal needs to be done with the left hand and not the right, so I start out this way). The STAY signal is as follows: Left hand and arm goes straight out from your side in front of you with your hand flat with fingers together, and then comes down briskly to right in front of the dog's nose as you say "STAY.".
Holding snug tension on the leash to keep the puppy from moving, pivot so you are standing toe to toe with the puppy. Smile. Encourage eye contact. Count to 3. Pivot back to heel position, release and praise. I do not move from toe to toe position with the puppy until I can do this with no leash tension and the puppy is reliably remaining still.
Then I work my way out to the end of the leash. During this time I am PREVENTING movement with the leash. If the puppy moves, I will put it back, and altho I do NOT repeat the stay command, I will give a POSITION reminder when I put the pup back.....GOOOOD sit.
Once the puppy is reliably staying with me at the end of a 6 foot lead (I consider puppies staying for 30 seconds without needing to be replaced often reliable) then I start mild distractions and putting the dog back.
By the time I take a dog to the ring, it can NOT be distracted from a stay position. Your stay exercise is only as strong as your proofing. A dog who is not proofed on a regular basis to the point of making a mistake is not learning anything as far as I'm concerned.
My last competition dog routinely did down stays on a busy street while I went inside stores to shop. A good stay is a marvelous thing for a dog to know.