All coders do some system administration as a matter of course, and the reverse is true as well. But to specialize in both is probably rare.
Respectfully, I think that once you start dealing with some more interesting problems, and doing so professionally, you might begin to realize just how much you don't know in one field or another.
In general, an expert program will not be a truly expert sysops because each of them is a deep field and developing truly deep expertise in either of them can be an almost all consuming task.
But, you can easily find people that are pretty good at both, and I would go so far as to say anyone who is good at one also already knows at least the basics of the other, they just might not be a true expert. Certainly anyone who is good at one has shown they have the right mindset and capabilities to become good at the other if they decided to.
Not all programmers are very familiar with hardware issues, or dependent on their area of programming expertise on network design.
I also found that many programmers are oriented towards creating new features, while administrators focus on running established tools at maximum efficiency.
While drawing on the same set of qualities, the interpretation of them can diverge.
Some people posses both sensibilities and the mind space to treat both disciplines well in environments and projects that scale. They are not common.
Those of us who get paged when the shit hits the fan tend to be pretty careful of breaking things; and quite often, we work on systems where relatively short downtimes can lead to losses greater than our yearly salaries.
That said, all the best SysAdmins have at least some background in C and NIX systems programming, and nearly all NIX systems programmers are also pretty good SysAdmins.
Then again, there are jaded "specialists" who don't dein to dabble in the "other" field, I'm sure.