He told you a half truth. It will bolt up to the head of any B series engine, that part he was telling the truth about. Where you'll run into a problem is at the other end where it needs to meet at the cat. Unless it's the DC model made specifically for your model Integra, it probably won't be long enough, or will be too short. As well as, as you suspect, it may drop too low below the oil pan and be closer to the ground than you'll probably be comfortable with, or not drop low enough to get underneath the oil pan at all. Not to mention, each header is designed to perform best with the engine/car it was designed to fit into, as far as primary and secondary diameter and legnth. These factors affect peak HP and TQ, and where they will be in the RPM range, among the main effects.
btw....93 GSR....sweet.