One of the downsides of being an NFL GM is you get tied to the players taken by your team, even if you weren't really thrilled about those players being taken. Put another way: different general managers have different levels of power and sometimes don't get final say.
For instance, there's an argument Ray Farmer, former Browns GM, wasn't the one who pulled the trigger on Johnny Manziel in the first round of the 2014 NFL Draft. (Manziel has already been released.)
After all, the Browns loved Teddy Bridgewater because science said so, right up until a homeless guy stepped in and convinced owner Jimmy Haslam to go Manziel.