Would the term 'full stack developer' really need explicit (i.e. Cisco) sysadmin qualifications?
What about more of the devops "get stuff working" on cloud platforms (EC2, Google App Engine, Heroku etc) using proven load balancing / caching / static serving software, changing your stack as and when you need rather than over-engineering something?
I used the CCNA as a proxy for the level of knowledge as the proper class room taught CCNAs do cover a lot of the basics from first pricipals.
eg how to design and build a small network (2/3k hosts) from the ground up starting with layer 1 the physics behind wifi, how switches STP Ethernet TCP/IP and so on.
Surly a full stack means dev you can go from the wire up to a complete application. In practice this means at least a CCNA.