One weekend I was on-call, we had a system we ran for the government, but authentication was handled by another government owned service, hosted and managed by another company.
A user called in early Saturday evening, saying that the system was down. After a bit of debugging, wondering where our alerting had failed, I concluded that the system was perfectly fine, but the authentication service had been returning 500 errors for around an hour. When I called the user back he made a comment that rather changed how I think about monitoring and systems. He says: Well, from my point of view it really doesn't matter which part isn't working, it's just down.