Curiosity hasn't killed that cat

Recently, Studs Terkel celebrated his 95th birthday, and he said, "Curiosity did not kill this cat" which is a great modification of the idiom (proverb) curiosity killed the cat. It basically means that you have to be careful about being too curious, or you will get in trouble or be harmed. So Terkel is saying that his curiosity did not kill him--he actually made a successful career out of it. Lucky guy.

But why does that phrase involve a cat? The earliest reference is from a 16th century British play, but it involved the concept of "worry". Shakespeare used it that way too. But

The earliest known printed reference to the actual phrase occurred in The Washington Post on 4 March 1916 (page 6): CURIOSITY KILLED THE CAT

because the curiosity of a cat literally killed it when it went somewhere it shouldn't have gone, was trapped, and died.

What I don't get is that people think the proverb means that people shouldn't ask too many personal questions. Sure, that's probably a part of the meaning, but it doesn't encompass its entirety.