A working DevOps group should be an amalgamation of the Dev team and Ops teams.
Trying to forge one team where everyone knows everything simply sets a level of mediocrity; you can research so far down an avenue in a given time, and get only so good at it.
I've learned from the ground up (i.e. electronics, basics of VLSI, board design, basic OS design, all layers of the stack programming), and went from there on to system admin. Then did a stint as a developer using the knowledge that I had from my earlier history, and found that the sysop area of my knowledge atrophied in the detail (and the devil is _always_ in the detail) the more I concentrated on being a better dev.
Went back to more of the operator/business side of things, and lo and behold, the more I go into systems and how to put together a proper reliable, recoverable infrastructure, the more my dev is atrophying. I'm half management these days, which means the ops side _and_ the dev side are both atrophying. The guys that do it in a dedicated fashion are more familiar with the latest tech than I am..
You can be a jack of all trades.. But I seriously hope a company doesn't rely on you to get them out of trouble when the fecal matter hits the fan.. If you've been spending most of your time developing, with the nod to tuning the servers so your app runs better, you're not likely to have been able to put the time in to develop the wider infrastructure to support things going fubar, or had the time and concentration to really work out what is likely to get you.
Having a few people marked as DevOps would be useful when you need to populate a middle ground.. They can work with both dedicated ops, and dedicated dev to ensure that scalability is baked in, and resilience is baked in to the apps. When it comes to ensuring the boxes are kept in tidy order for everyone, and get to be able to recover from the smoking ruins.. That's where the dedicated ops shine. When you really want that app to do something really slick, that's when a dedicated dev shines.
Small scale, a DevOps person would work. The larger you scale, the less appropriate it becomes (as the only solution; a big company with the techs being solely a DevOps team would scare me).