To me, a Full Stack developer takes responsibility for the full stack. When a problem arises, she doesn't say: * It's a database problem. Call the dbas. * It's a network problem. Call the network folks. * It's an app server problem. Call the ops team. * It's a user interface problem. Call the UI team. A Full Stack developer first says, 'This is my problem until I can locate the problem and possibly identify someone m…
To me, full stack means front end + back end -- can write good CSS and can write good queries. Knows how JavaScript's "this" works, and can intelligently converse about data sharding.
Database administration, network problems, app servers -- these are most certainly NOT part of a full-stack developer's knowledge, any more than fixing the oven in the company cafeteria. And I wouldn't want a full-stack develop touching the company's network configuration or trying to do database administration on high-load production servers under any circumstances -- there are very good reasons that those are left to specialists in these areas.
Of course, it's possible you could have someone who does both full stack and DBA, or full stack and knows a lot about networks, but that has nothing to do with full stack. The "stack" web developers are talking about is, for example, LAMP -- Linux, Apache, MySQL, PHP (or pick your own stack), and it's about being proficient in all the layers of that stack, when writing applications -- not running servers or networks.