I think its the bipod on the table that they object to - when I brought my 1919A6, I wasn't allowed to shoot it. FWIW, though, they gave me no hassles about other .308 shoulder fired machineguns. Bren? Maybe...
And oddly enough, one time while I was there they allowed a guy to clamp his handmade Gatling gun (in .30 carbine) on the table and crank it off that way.