The author titles his post "Never accept a counter-offer", and says: "By saying you have to be prepared for it, I meant that you should never accept a counter offer."

Just because he later contradicts himself, doesn't make it good writing. You can't have it both ways.

The way I see it with the author stating "(your cat dies and you need bunch of money to save her)." is that only the person that is in the situation can assess the situation. The article talks broadly, but one should still take that particular situation (edge case) into consideration. Tough, it's rarely possible to judge an outcome correctly.