My friend is possibly looking at acquiring an AR15 that has a 37 mm grenade launcher attached to it.  I have told him that to the best of my knowledge, it is ok to buy a grenade launcher but the grenades themselves require the paperwork and the tax stamp.

Is what I told him correct?

I am looking around on the Internet to try to find some more information, but I thought that I would also check here.

The 37mm don't shoot grenades, only the 40mm which is of itself a destructive device. And yes, the grenades themselves also require paperwork and a tax stamp, as well as special explosive storage requirements.  
The 37mm's are flares and gas launchers.

If it's a 37mm, it's a "flare" launcher and not a grenade launcher and is OK to own without any paperwork.  A true 40mm M203 requires a $200 tax stamp as a destructive device.  Also, any explosive grenade with >1/4oz of charge requires a $200 tax stamp.

The other wrinkle is if you own a 37mm GL and anti-personnel ammo (buckshot, beanbag etc), then you have a destructive device even though it's really a flare launcher.