The statement "Schools should not have a NO TOUCH policy" seems pretty clear ...
But does it say that we can hug them? No. There is a world of difference, litigiously, between a pat on the back as a well done, or a consolatory shoulder squeeze, and a cuddle. Don't get me wrong, I believe children should be hugged and cuddled as much as they want to be, and that practically everything can be made to feel a bit better with a cuddle and a brew! What I need to know though, is that I'm not going to get grief from parents or management about it.
To go back to the original point of your debate about touching, there are not many finer moments as a parent than having a snuggling child sprawled over you whilst you share a story with him or her or them. I would love to give that to some of the children in the school who have very little positive physical contact. (I'd love to have the time to share a story with all of them lol, not just some, but some need it more than most!)
However, we are in a culture in the local area where this is not permissible, where story-time in Juniors is being eroded because there is not an identifiable learning objective, success criteria, or APP measurable outcome, where it is not seen as an "efficient use of teacher time." I can read to them in the literacy hour, or they can read to me in guided reading. I perpetually argue this point with the literacy co-ordinator because an enjoyment of books is not going to be fostered by the current policies. Without an enjoyment of books leading them to go further, then a whole world of learning and entertainment is locked off to them as adults.
I'm biased though. I have an enjoyment of books that means I'd rather read than do a great many more boring thing (like sorting out the washing pile lol!) But then I had a childhood swamped in books, and hugs. I got lucky.