I don't think I said it did?
The only way anyone can die from a "broken heart" is if the heart is physically "broken".
However I believe when someone is left utterly bereft and sees no future after some catastrophic life event, they can descend into the absolute depths of despair and just give up on life, stop eating, stop functioning, become reclusive and just "fade away".
Is that the same thing as dying from a "broken heart" Possibly.