[bo1024]

The point is that when it "never stops", there are models of ZFC in which the "infinity" number of steps it runs for isn't considered infinity by the model, it's a made-up "nonstandard" number that is smaller than infinity but larger than any integer. And that model considers that to be "halting", so that model says the TM halts.

[wat10000]

That’s just a change of definition. That isn’t really saying that BB(748) is different under a different model, just that there’s a BB’ equivalent for that model and BB’(748) is equal to something else.