It seems like you're still using some form of automation to find bugs, regardless of whether these would be classified as unit tests, correct?
That's certainly not unit testing though.
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.