I think that's being too extreme and dogmatic. Unit testing and small-scale integration testing (implemented as unit tests) are a way of testing your assumptions and documenting and communicating your assumptions to others. Both are good engineering practices.
You just have to be pragmatic about how you use these practices. Teams definitely get too dogmatic and narrow minded about mock-heavy unit testing, and some people do manage to write code without writing any unit tests, however those are both extremes that are best avoided or of only limited applicability.
The benefit of unit tests is that certain things are more economical to test that way. You literally can test everything though integration tests of varying levels (or manual testing!), but it'll take more effort and run more slowly. If you want to thoroughly test a regex, just test the regex by throwing a dozen strings at it. Don't bootstrap the program and construct valid input requests to test each of those strings (but do do that to test that everything can work together, which includes a subset of those strings).