People are really skewed either way on this topic, and, as a parent I suppose I can understand why. It is honestly the hardest thing to do, that is, punishing your child. Do they cry? Often, even if you just raise your voice to them. I didn't find the hotsauce to be out of the line, if the mother has honestly tried every other tactic under the sun and it didn't work.
As most parents, and most parenting books, and most psychologists will say, not every child is the same, and therefore your tactics at discipline must adjust accordingly. While Dr Phil's wife makes an excellent point in her video about the mother promising such and such, so too does it need to be realized that a we, as a society, start hitting a pretty slippery slope when we try to define the 'do's and don't's' of discipline. When does a spanking reach abuse? When it leaves bruises, when it's done in anger. Clear cut. What if your child does not respond to spanking? What if your child does not respond to time outs, to bribes, to a rewards system?
I think there is more to this story that anyone can really judge, without knowing the child and his behavior, and the mother and what she has gone through.
So at this point, I suppose I must join the fence. I will say that my children wouldn't be able to handle hot sauce. I can't stand the stuff myself!