Overflow incontinence happens when your bladder gets so full that the sphincters physically give way and you pee yourself. In other words the muscle would give before the bladder ruptures. I came across a thread about Tycho’s death on Reddit and virtually no one was calling bullshit on the story that he died of a burst bladder because he was embarrassed to go to the bathroom during a banquet.
I don’t know the particulars of this specific person, but you can absolutely have your bladder rupture. Conditions like neurogenic bladder can cause routine over expansion of the bladder, weakening its walls, and eventually it can tear.