Depends on the structure of the org.
in my experience your Systems admin doesn't typicaly manage the webservers because the rolls are so different. SA's are more to manage the network. A "Webmaster" usualy handles everything web related, web server (iis, apache), the technologies on it like CF, PHP, ASP (MS systems), jsp and so on. Like wise you'll probably have a DBA to manage the DB servers, because the rolls are again quite different. You can have a DBA that knows the in's and outs of oracle and SQL server but not know anything about how a web server works. Again this is just the experiences of what i've seen, you may get a few different configs from other members.
If you don't ask the right questions, you don't get the right answers. A question asked in the right way often points to its own answer. Asking questions is the ABC of diagnosis. Only the inquiring mind solves problems.
-Quote by Edward Hodnett