How do you know Ricardo? The very first signing made when Rafa was coming in was Djibril Cisse. That wasn't a player Rafa asked for or wanted, he was signed before Rafa in principle, but he had been planned for at least a year before Rafa even thought about Liverpool.
How do we know there weren't others. The Robbie Keane situation springs to mind. It does make you wonder...
I'm not saying Babel wasn't his signing, in my opinion he was. But I wouldn't agree that every player signed has been Benitez's choice.
Cisse was Houllier's buy that was already arranged and in place. It wasn't a case of Parry or someone else choosing a player and forcing him upon the manager, it was still the case of the manager choosing the player. In that case it was Houllier. It just so happens he was gone by the time Cisse showed up.
So simply there were not others because Houllier had not arranged any others in advance.
The other example you gave was Robbie Keane. Benitez did want Keane. However it didn't work out for a few reasons. One reason was that he also wanted Barry as part of the same side, so not getting Barry reduced (in the eyes of Benitez) Keane's usefulness.
Every player we sign has been signed because the manager has said he wants them. That is the way things are done, always has been. You can doubt this if you like, but you would be totally incorrect to do so.