Considering that BB is the GM, not Caserio, you kind of don't have a point. Caserio is the Director of Player Personnel. Caserio was promoted to that Position on February 21, 2008. This was to start integrating him into the draft process while Pioli was still around.
2010, 2011, and 2012 and 2013 are definitively Caserio's.
2006, 2007 and 2008 were probably the 3 worst drafts in the Belichick era for actual Picks, though 2007 was arguably the worst draft in the modern era for players available in general. What was going on at that time? Well, for the 2006 draft, we know that the Scouts and position coaches had their feather's ruffled when BB over-road them to take Maroney and Jackson. Then you had all the rumors of Pioli leaving for almost 3 years, which I'm sure unsettled people. Then you had Pioli AND Dimitroff leave in 2009 and 2008, respectively. That upheavel certainly didn't help matters.
Since then, however, you can see the progression as Caserio and the changes in the scouting department got in line with Belichick and things have been better.