While I would call such tests unit tests, the reliance on critical dependencies from within the test code is often problematic. Besides being slow, critical dependencies also have another nasty property: We can't ensure the availability of the resource being dependent on.
For example: When running the tests against a test server, the server needs to be up and running. In case the server is shut down, or perhaps even taken away we are no longer able to run our tests.
Other typical examples of critical dependencies involve calling native code from Java or direct execution of shell commands. In such cases the problem can even become worse than 'being slow' because a dependency on native or environment specific code may prevent to run the tests from a pure development environment.
Now while critial depencencies are definitely something one would try to avoid, developers often need to accept to live with them (at least for some time), as they are working their way through bringing their codebase under test.