That tube over the gun barrel does sound hokey to me. I know of no medium caliber military cannons that use the tube-over-barrel-and-muzzle brake arrangement.
My extensive field experience servicing military medium caliber automatic cannons supports KN's view. The high velocity gas exiting the side ports at the muzzle brake must vent freely and be directed to "pull" the barrel in a direction opposite to the recoil impulse for recoil reduction. As I recall, in working with the 25mm M242 Bushmaster automatic cannon, the difference in recoil impulse between firing with the muzzle brake and without is some 40% recoil reduction. End users were advised that continued firing without the muzzle brake would cause damage to the gun's hydraulic recoil damping mechanism. And that is with APDS-T ammunition with a muzzle velocity over 4,200 fps!
I suspect that for small arms, any percieved recoil reduction from using the barrel tube is simply from the increased weight of the tube itself.