I thought Koeman wanted Sigurdsson since the summer he came in..? I thought there were rumours or stories of that nature even back then. He didn't particularly rate Barkley at any stage is my personal opinion, hence all the calling him out comparative to other players.
So Koeman (IMO) wanted him out and we ended up with Rooney, Sigurdsson and Klaassen coming in.
I'd genuinely love to know the backroom thinking and who was pulling the strings on those picks. If any of those three was a vanity project for the sake of the board you'd have to wonder about Rooney. I tend to think though that wasn't that either, we were likely approached to see if we were interested and it went from there. Koeman always seemed on board with that one too. In fact, Koeman seemingly was on board with all of them...he only seems to have put his transfer problems at the feet of not getting in Giroud. To a certain extent, his plan while not probably leading to awesome football would have been a fair bit better with a player of that ability up front. So I doubt Sigurdsson was a misstep to him.
Overall though, I don't think aside from media interviews there has been any sign of Moshiri interfering in the transfer plans.