Proof of the exception does not prove the rule.
I think we all know that straps are useful tools, but for people who over-use them (just like people who over-use belts), they do nothing good. We've all seen that guy in the gym. You know the one-he's in the corner, with gloves, straps and a 2" weight belt going to town on the adductor machine.
I have some friends at the gym who insist that their hands are just too weak to do deadlifts without straps. I don't argue with them, but I bet if they sucked it up some, and did their Dls bare-handed that they'd develop the hand strength required to perform their DLs.
For someone who has grip trouble (like the OP), I'd suggest backing off of the gear-the wrist wraps and the bar straps are only allowing him to lift more than his native grip will allow him to, and in the process their grip will not progress.