"There are several aspects of the game which are just stupid. For example I seem to be buying all my weaponry from a POLICE OFFICER at THE POLICE STATION. "I don't know what's going on here, but I guess I just have to trust you" he mumbles, as he sells a Katana to a teenage boy. "Everyone tends to be more trusting in Persona 3. Everyone's confused about the strange stuff going on, so they're more willing to unusual answers and that kids would need weapons to deal with the problem.
In Persona 4, the threat is obvious. Someone is going around killing people. It could be anyone, so no one ever fully trusts anyone. They never let anyone outside of their group know what they're up to. Not the police, not family, not other friends, because the murderer could be anyone. In Persona 3, it's not clear what's causing the apathy syndrome, but they can be reasonably sure that it's not the result of any human. So they place their trust in each other, Ikutsuki, the Kirijo Group, and even Officer Kurosawa. SEES knows he won't pose a threat to them, and Kurosawa hasn't seen any negative result of selling weapons to teenagers. There are lots of weird things going on, but none of them involved weapons obtained from Kurosawa. There's no guarantee that he really can trust them, but he's willing to help them out if they really believe they can eliminate the problem. The Kirijo Group has also done research on Shadows, so if he really needed proof it could probably be provided.