Interesting topic of discussion.
I would say there is some evidence to suggest you are onto something here, no doubt.
One thing working against this theory, though, is Whaley not getting it when it comes to the draft and throwing picks away to move up. He should be doing that the other way around because, as you say, it's more valuable to get more kicks at the can.
It's also worth noting the Patriots seem to pursue a similar scheme, because they have to shoot for undervalued guys b/c they are always drafting so low.
But they have a different spin on the idea. They are looking for overlooked value not in the form of bad character or injured players, but in the form of what they perceive to be good or serviceable players not on everyone's talent radar.
They also place an emphasis on intelligence/character over raw athleticism, which seems to work well. They want guys who can take orders, follow a plan, slot into a system, and not screw it up with meathead play.