Mechanism of Hofmann Rearrangement Reaction
Water is present in large excess when compared to the amide, so it is statistically not likely that the proton would be removed from the amide rather then water. Even if it happens, proton exchange is reversible so it would be formed/unformed many times that eventually the removal of the proton by water would happen and proceed with the mechanism.

Regarding the attack to $\ce{Br2}$, I believe the reason it doesn't happen is that the ion would be surrounded by many many water molecules because: 1) the amide forms H-bonds with water, 2) the ion is solvated efficiently by water, so more molecules would be around to have their protons removed.