[mumblemumble]

Whether, in practice, I would consider them to be unit tests probably depends on what my colleagues want to call them, and little else.

Personally, I do prefer a more classicist definition, because I believe that's the more pragmatic one. But I also believe that arguing over the definition of the term "Unit test" is one of the most wasteful possible examples of bikeshedding. Like you imply, the only thing that really matters is the extent to which your test suite gives you confidence that the software behaves correctly.