But Amaro acquired Halladay and Lee and Oswalt (and then signed Lee again). And Papelbon (not a fan of him or overpaying closers but he got results).
The difference and time period you cite was not Gillick taking over from Amaro, it was Gillick taking over from Montgomery.
And really Gillick's trades and FA signings from when he was actually GM don't look especially brilliant. Other than Lidge, Gillick's strength was the small deal paying off big (Werth, Feliz, Moyer, Blanton, several relievers). But OTOH: Flash Gordon, Adam Eaton, Garcia.
Amaro always had Gillick's support, and the reason he wasn't fired sooner is because he was doing the job as the owners wanted him to do it. It was only when they finally realized their mistake that they held him accountable for his (after first forcing out Monty just as Giles was forced out for Monty).
Which is also why some are willing to find a grain of truth in this gossip; it's not hard to imagine John Middleton and Ruben toasting the Howard extension at the time, or celebrating the signing of A.J. Burnett over cigars.