I don't have a Model 12 so I can't be sure, but Remington used 6 groove RH twist on their other .22's, so I think it is safe to assume the Model 12 was no exception. Twist would have ben 1-16 for the LR version, 1-24 for the .22 Short. They also made the gun in .22 Remington Special (the Model 12CS); I have no information on that twist rate.
If you mean John Browning, he didn't make any barrels for Remington or anyone else. He didn't even design the Model 12, Pedersen did. If you mean Fabrique National, I doubt it and can't see why Remington would need to buy barrels from anyone else.
If you are looking at markings, let me only note that a barrel is a barrel and gunsmiths often replaced a shot-out .22 barrel with whatever was handy, so a strange or mismatch barrel on a .22 is not uncommon.
Jim
