He was charged with DWI as a minor, he was arrested for "Acts Prohibited" a violation of the Controlled Drug Act, information keeps dribbling out, He needs to take a trip to the District Court and get a copy of his file. He might not remember the charges that local PD threw at him. He may only remember the DA's plea bargain, but even with what you have mentioned so far, the court may uphold the chief's decision.
Please note that "Noting RSA 159:6 does not define "suitable person," the court stated, "However, we have construed the term to give some measure of discretion to the issuing authority to deny an application if it deems the applicant to be unsuitable." and also note that a conviction is NOT required.
See NH Sup Crt Case No. 2015-0003, Derrick Horton v. Keene PoliceDepartment
(See also Case No. 2015-0350, Thomas Newman v. New HampshireState Police Permits and Licensing Unit,)
(See Also Case No. 2013-0875, Alexey Obukhov v. John Bryfonski)