This is from the thread I linked above
The "Flip" which Burrard discussed was not the rise from recoil. It rather was a downward flexing of the muzzles which occurred as a result of the inertia of the muzzles trying to stay stationary as the gun rose in recoil. This would offset to some extent the recoil rise causing the gun to hit lower than it otherwise would. This flip, flexing or bending of the bbl (call it what you will) is a different thing than recoil rise.

I have Vol. 3 of the 1948 edition of The Modern Shotgun and the discussion regarding "muzzle flip" is in Vol. 1 p. 223-227. He stated in Vol. 3 that short barrels gave a different "flip" than longer barrels and tended to shoot higher.

A SBT video and there is clearly a slight downward muzzle movement as the ejecta leaves, and before recoil rise