I would describe myself full stack under that definition. Most "full stack" people I know that sit in my Uni courses have mostly learned Java EE + Oracle DB or Javascript + /dev/null^w^w MongoDB. Most of them would probably not be able to construct a relational database or libc from scratch.
Granted, such knowledge isn't immediately useful since it's something I or anyone is likely to do but it grants insight into systems. I know roughly how a query optimizer does and what it can, and more importantly, can't do.
When you know a system you can optimize for it. When you don't know a system you can only follow someone else's advice on how to optimize for it.
Isn't the current quest in quantum mechanics (to find a grand unified theory) to find an abstraction that does leak? At the moment it's too self contained and doesn't explain anything about the macroscopic world.
In any case, having a basic understanding of the next level up (the electron) has proved quite useful to my career, otherwise I wouldn't know how turning things off then on again affects the machines I'm working with.
If you are claiming to be full stack you better be prepared to go all the way.