Well, first off is the obvious visual difference: mechanics are often dirty, wear ragged uniforms, and typically don't have the best grammar or vocabulary. Few have even been to college, let alone graduated.
Admins, however, typically did there time at a respectable institution, wear clean close, don't get greasy, and talk better than mechanics.
Furthermore, there are the respective positions: mechanics spend much time on their backs, or with hands jammed elbow-deep into an engine, which is subconsciously a less-than-graceful image. An admin, though, does most of his work sitting or standing.
You also need to consider the horror stories people tell about mechanics who rip them off. It's on the news all the time. However, in my life, I've only seen one story about computer repair fraud, and it was in a Best Buy, which you would expect (since it's a bunch of teenagers, not respectable admins).
I'm no big deal admin, at least not professionally. The biggest job I've undertaken is configuring Linux to be a masquerading server for a home LAN. I know my way around Windows and Linux, and could be an admin if I were interested. What you say is true; that for the most part, it is just mechanics' work to keep a network going. But the fact is, people who work with cars are less educated than people who work with computers. Public perception does not depend on what could be done--it depends solely on what is done.
I, for one, would love to understand cars the way I understand computers. I can't imagine anything more fulfilling than being able to repair my own automobile, just like it's fulfilling to repair my PC. I take pride in knowing that I'll never have to call in the so-called "computer expert" to tell me what I've done.