No one is saying they are not part of the BT Group however under OFCOM rules Openreach operate as a separate company so as to provide an equal service level to all providers and that BT Retail gets no preferential service this link may help you further http://www.expect.openreach.co.uk/ also Retail and OPenreach have their own CEO'S
each are separate entities ,albeit part of the overall BT Group, so complaining to BT retail about problems with openreach are not going to get anywhere. Probably because OFCOM made them treat each ISP the same and cannot be seen to favour BT Retail
much like going to B&Q and complaining about a problem you have with screwfix - both part of the overal Kingfisher Group
I do agree though that openreach are a will unto themselves and should be more accountable. unfortunately as openreach have a monopoly on the lines there is no - I'll go somewhere else
'The customer just wants their problem resolved and they don't care who is who.'
Then why bring the debate of who works for who?
The BT Group own hundreds of different companies all over the world, all operate independently from one another. That's how Corporations work.