"I'm not in a position right now to tell you what my position would be, one way or another" is not an adequate answer to the question of whether or not non-prohibited persons should be issued a CCW.
Although I do agree with him that each application should be decided on a case by case basis: "In this case the applicant is not prohibited. CCW approved" "In this case the applicant is prohibited. CCW denied." As much as background checks both suck and do nothing about keeping criminals from possessing firearms we might as well make use of the pesky things.