Myself, I would regard "NHS Supply Chain" as just another supplier.
I believe it is operated (on behalf of the "NHS Business Services Authority" - whatever that is) by DHL Supply Chain, which is in turn part of Deutsche Post DHL Group!
I would suggest that to use the term "NHS" in the title of any for-profit business is, shall we say, rather misleading. Similarly with a number of other semi-commercial "ventures" that like to emphasise the
NHS bit.
It's a bit like a company wholly owned by the Secretary of State for Health (eh? how does
that work?) calling itself "NHS Professionals Ltd." ... or Geoff Hannis & Co. (Geoff and his mates) calling themselves "NHS Biomed Services"!