When you don't expect much at the start, one person can do programming or sysadmin job first - if you're just hosting your own page without any special features. If you get to the situation where you have many servers to take care of (5+ let's say), then sysadmin simply becomes a full-time position that needs someone experienced with this environment. Someone who's mainly a programmer may not have enough real-world experience to deal with the potential problems, or might not know where to look for solutions. If you require quality, you'll need specialists at some stage.

Splitting the roles is also practical. At some point you may have a project deadline coming soon, when suddenly (for example) network fails - do you really want to send experienced programmers on a trip to the datacenter in that case?

Really, it's a question of how big you are and how much time does your infrastructure need...