Children can and do start to need deodorant from a fairly early age. Mini Boo was about 8 or 9 when I needed to start buying it for her.
I'm not sure why people who have been quoted in the article are saying it's expensive though. My local poundshop (these are everywhere!) sells toiletries from as little as a quid per item. In fact, no brand, equally as good as, deodorant is sold two for a quid!
That being said, if the teachers say there's a need for these items to be doled out to children, then that's obviously the case, it serves no purpose for them to lie about it. I just find it disgraceful that parents are failing to shell out a few quid to stop their child being singled out in school.