This is an over simplification of a common problem in the IT industry. There is simply too much for any single person to know everything, so people specialize their knowledge. Ideally only those with the specialized knowledge to do a task should do so.
In the real world, we are often asked to "wear multiple hats" by management structures that still don't know all the complexities of how IT works and are dealing with the complexities of the company operation and finances they do know (and often the IT staff doesn't).
This often results attitudes like those asked about by the OP when two of these IT fields overlap. Like that attitude, as a network person, I know how easy it is to have similar thoughts about sysadmins, as often sysadmins are asked to manage the network as well.
In a relatively small number of cases they do a great job and in another relatively small number of cases they do a horrendous job. Most of the time, they fall into doing a decent job somewhere between the two. However, it is not the great jobs that are remembered, it is the horrendous jobs and to a smaller degree the decent jobs that are remembered.
When a network person is brought into the mix (either a consultant for a specific reason/project or because the IT staff has expanded and now includes one), they often find ignored recommended best practices, misconfigurations, security holes, etc. They spend a great deal of their time trying to figure out how the blank things got the way they did, troubleshooting problems that should not be occurring, and fixing misconfigurations and problems.
But this goes both ways and includes a number of overlapping disciplines. Specific to my example, I know as a network person that I cannot set up a server as quickly as a knowledgable sysadmin and/or that there will probably be a number of things I would overlook or do incorrectly (or at least not in the best way). Give me enough time and I can do at least a pretty decent job, but often the job/work does not give that time. If I have the choice, easily my preference is to hand it off to a good sysadmin.