I've never found that to be true. People love stuff being done a lot more than they hate looking bad. Managers at big companies know it costs almost as much as a programmer's salary to find a new programmer, so if the only problem that you're causing is doing extra useful work, they are not going to make it a priority to fire you and find someone else who will do what they're told. In fact, managers are often so overextended that a self-managing employee that's visible to the rest of the organization is an asset.

(This worked for me when I was at BofA. I worked on a tiny team that nobody cared about, but people pretty high up knew who I was. This was generally good for my manager and her bosses. The impression I got was when I was on a conference call, I was the only person who ever wrote code to solve problems, and people seemed almost grateful for that. I didn't really enjoy this, and there was a lot of red tape and bullshit, but I do know people who do fine with this kind of job. YMMV.)