This, sadly, has the makings of an unhelpful division. No-one is saying it's OK to hit, slap, smack, tap, whatever you want to call it, children. Most recognise how bad this is for children, but this dear little chap is not being hit regularly, and his gran doesn't think it's OK.
What most are saying is that the odd lapse is not deeply damaging in the long term. We are mostly basing this on experience.
That doesn't mean that the research quoted is wrong, we are just putting it in context.
It is of course true, as some of us sadly know, that some families use the 'one small tap' defence, when a child is being abused. I am as sure as one can be on a forum, that is not the case here.