Well partly true, but the question was about a sysadmin job, not a software development job. Sysadmins probably would need to write small shell scripts or whatnot, but they probably aren't going to be designing and building major new pieces of software. Rather, they will be configuring, deploy, and administering software that has already been built. It's a different skill set. And even in the real of software development, 99% of the developers out there will not need to ever design a new language or a new OS.
With that being said, I've found that with a few notable exceptions, most of the good software developers I've worked with have degrees (although one of the best I've worked with doesn't). I will also say that almost all of the poor software developers I've worked with DID have degrees -- and some from supposedly top-tier schools. It matters a great deal where you get your degree from, not in terms of the name on the diploma but in terms of what is emphasized in the curriculum. Some colleges get this attitude about anything applied. People who come out of those colleges may have an advanced understanding of the theory of computation but tend to have a lousy understanding of object-oriented design, system architecture, usability evaluation, low-level systems design, etc. -- the things that matter in the "real world".
That's not to say that it isn't good to learn some theory too -- just that the VAST majority of students are better off understanding how to design and build real, useful software systems and keeping the pure theory to a reasonable minimum. Unless you're planning on doing graduate research in theoretical computer science, my suggestion is to get a degree, but to try to get a degree with a more applied (although not exclusively so) focus. For sys admins, a tech degree might be sufficient if you don't already have enough years of experience. For a software engineering role, you'll probably want to get at least a four year degree, or a master's if you want to do more advanced stuff.
With no degree of any kind, you can probably start in desktop support or a help desk, if you're okay with that.