For instance we had a rule at a place I worked, where we needed to have 80% unit test coverage. And what is described in this article happened. Anytime we'd make a small refactor, we'd have to go update 3-4 test libraries. And if it was a big one, then you have a lot of tests to update. And since some were complex (or since there were a lot of them) people didn't dig into that much. When people finally did it sometimes showed the test wasn't even testing what it was supposed to anymore.
The other issue is we had a lot of bugs around the integration of data. For instance if the DB class returned back an empty array vs null vs empty string. When we did the unit test we mocked it to return what we thought it should, which may not be the correct one. Integration tests better caught this, functional tests even more so.
It seems a lot of shops don't use tests at all, now working at places that have done both, I'd rather error on the side of fewer tests, and do it smart instead of hitting a metric and assuming your code falls into line.