You CAN run a 37" underneath the bed (at full PSI), BUT you need to have a custom hitch fabricated (Carli doesn't make a "Trophy Hitch" for the RAM).
ALSO, I believe, you have to be running a flatbed (rather than the factory pickup bed) because the added hitch length will interfere with the factory bumper(?). Perhaps this is why Carli doesn't make a Trophy Hitch for the RAM. (I think the fit issue on the RAMS is not width, but length. HD Fords have slightly longer pickup beds.)
All this said, I am positive that you can run a 37 in a custom hitch under a flatbed, because I am doing exactly that.
Specifically, my setup is Ram3500 CrewCab Short-Bed with OEV AlumaTray in place of factory bed and custom hitch to fit 37'.