I've worked at a job where the problem was the exact opposite of these two statements -- the directory of the department had been a consultant -- he believed that the solution to any problem was to throw bigger hardware at the problem, and that the tech folks were just an annoyance that he had to deal with.
I've had similar experience.
Some of the very best managers I've worked with have been completely non-technical. Some of the very worst managers I've worked with have been ex-techies.
In my experience the divide between good and bad management has very little to do with technical experience, and a lot to do with being able to trust people to do their job well and remove the things that stop them doing it.