I think that person was talking about having had 4 out of 5 squares in a line on their bingo card already, and stumbling across "baby+bathwater" earned them bingo. The card is metaphorical though... more of a mental buffer that just overflowed.
Mine too, and I think the post is fine also, but I have some idea of what that person was talking about. For a while, in some corporate environments, it was a recurring phenomenon to hear someone dismiss an urge to be cautious by saying "You're throwing out the baby with the bathwater."
So I can see where someone might count it toward buzzword bingo. But this post also offered an alternate solution when saying "baby+bathwater", so the bingo caller should refuse to score this one.