It sounds like a collaborative process. This is what Ancellotti said about Doucoure that you referred to:
"When we started to talk about the transfer window, Doucoure was on the list of the club. He was not on my list, but we talked together and we both agreed to sign him".
Our model seems to be that both manager and DoF have to jointly agree on a signing, and there is some logic to that as neither can go awol and start bringing in players that the other doesn't want.
I find suggestions that Brands has no say in who we sign absolutely preposterous. Brands has a direct line to the club's accounting and sensitive information on budgets and what leeway we have on contracts that we can offer etc. The manager is clearly empowered to choose their own targets but Brands has to authorise them and ensure that our budget can accommodate them.
He absolutely is accountable for all signings because even if they aren't his recommendations, he will negotiate the price and determine the contract so he is absolutely open to scrutiny for every single signing we've made since he's been here - the good, the bad and the truly ugly. My simple theory is that he's rubbish at his job and happy to go with the suggestions of very experienced managers. He brought in many more players that could be considered 'his picks' when Silva (very inexperienced and fresh off being sacked by Watford) was manager.
And as far as I'm aware, no reputable source has ever suggested that Moshiri went completely above board and signed Iwobi or Tosun without the DoF's consent. Tosun was believed to have been on Allardyce's radar when he was crystal palace manager and Iwobi is most likely a Brands panic buy after missing out on Zaha. Our recruitment process is enough of a mess already without muddying the waters further.