ultra-pedantically: that's true with the "well tempered" tuning that is used almost universally. But this is really just an approximation, and one that our ears have grown used to.
Mathematically speaking, B# <> C. On a piano or other instrument that quantizes tones, we have little choice but to go with the approximation. But for violinists and others that can choose from a spectrum of tones, it's possible to hit those tones exactly. Of course, when playing with others, the violin still needs to quantize just to be in tune with the others.
bflat triggers a lot of engagement on Twitter and elsewhere because everyone wants to correct it. Couldn't have chosen a better name.