Probably not? I think they are intentionally calling it the relative minor, not same note, which makes a kind of sense in the usual way punny names do (i.e. a bit of a stretch, but not ridiculous).
Edit: Actually B♭ minor is the enharmonic equivalent of A♯ minor. IE another case of things in music that are the same but aren't.
slowly backs away
And now I'm down the rabbit hole of reading about tuning systems again.