No, that's a misconception. If you add BB(748)==‹any N but the correct number›, you get an inconsistent system that will either claim that a machine doesn't halt even though it does (e.g. the real BB champion), or that some machine does halt at N steps, which you can then disprove by enumerating all the turing machines of the relevant number of states for N steps, and showing that no machine halts at that step.

Either way, the only BB axiom you can add without blowing up ZFC is the correct one.