Sure, some of the monitoring systems I've written do some fairly detailed testing. For example, I wrote the Justin.TV chat system. There's a group of bots that periodically log in to the production chat server, send messages to each other, and email me if anything doesn't work.
I speak only for myself, but I would say the following: The real key is fully automated testing, no matter how it is done. The finer the grain, the better, generally. Matching an actual business case is near ideal.
Fully automated is necessary so you can run them frequently, automatically, near-continuously.
But beyond that, I think you get into religious territory, and I think people getting dogmatic about the definition of "unit test" tends to mistake definition for virtue (a common failing). If you've got automated testing, great! You win. Doesn't matter how it works.
Or, rather, it does matter, but only within your context, which nobody else is really competent to judge you on.
Yeah, the only thing that matters to me is whether the pro-unit testing position has become more religious or whether the anti-unit testing position has become more religious. I'll take whatever seems serious. I liked what Joel Spolsky had to say yesterday but I disagree with the linked blog post today.
That's certainly not unit testing though.