I agree with your basic point about parents being the ones mainly responsible for a kid's upbringing. However, I simply see the separation of verbal and physical discipline as an artificial one. If we allow teachers to exercise discipline in the classroom at all, then also allowing a clip round the ear or a ruler across the hand etc. is not unreasonble.
I don't see it as an artficial one because everyone asscociates verbal correction with everyone else, even at a young age we do it for eachother and so do all adults, or at least there are times when they should, but physical discipline is different, parents have a natural authority over their children and so have the right to take discipline to the required levels and children naturally understand that they have to submit to them, this isn't the case with other adults, not even teachers, which is why kids often scream in rebellion 'you're not my mother' or something like that.
However teachers do not have that personal connection with children in spite of the authority they have, I think if people outside the family unit begin issuing physical punsihment it can create confusion for a child and be counter productive, especially if their parents disciline them in a different way, which is not something a teacher will be aware of.
The key in my view is consistency, I would say that children need the primary source of guidance in their lives to be consistent and from the same people so they come to have a respect for that person(s) and adhere to the standards being taught.