We don't know that. It's also difficult to judge each transfer on its own if the manager plans to sign two or three players who would compliment each other, and we only sign one of them.
On the latter point, you sign an entire squad to complement each other, and no manager gets every player they want. Signing a player who will not work without his 'partner', if that partners's not already at the club, would be foolish in the extreme. (and even if you get both, what if one gets injured?)
On the former, I think we have good clues. Player's we're linked with early, are clearly pursued and ultimately signed, were unanimous, or near-unanimous, committee (including the manager) choices. Players we revert to late in a window are likely lower priorities and may not be a unanimous choice. On that basis, Lallana, Lovren, Moreno and Can were all unanimous or near-unanimous targets. One wonders whether it was manager or some other member(s) of the committee who were less sure of Bony or Shaqiri, for example.
But there's an issue here with regards to Rodgers' defensive nous - and one about his man management. We can easily read into the circumstances that he wasn't convinced by Sakho pre-purchase (when Papadopoulos was first choice); but he really can't/shouldn't carry that through into ignoring his performances and not using him. We as a club can't spend £20M on the committee choice one year, then the same on the manager's a year later, casting the former aside.
But seriously, which is the better player? The committee structure - or the manager's use of players it brings in - certainly doesn't appear to be operating well, but there's a lingering suspicion that it still has a better eye for a player than he does alone.