Seems like the wrong charge for the particular reason they're citing. The reckless conduct involves accusing him of lying on paperwork that was involved in a sponsorship or character witness type thing needed for a gun license. So the proper charge there would probably be along the lines of lying under oath.
The reckless charge could still be a thing but would probably have to involve other evidence not just being involved in the process for the gun license that the state gave the shooter.