Everyone else only has a full copy of the repository if they actually check out a copy and keep it local. That's apparently not how my coders do their workflow.
The most usual way to work with git is to pull a local copy of the whole server using "git clone"[1]. The only way to do a partial copy would be to do a shallow copy locally with only the last few commits, but then it will probably be harder to merge back... So it seems you are either wrong, or that your team is using a very very exotic workflow.
[1] it is explicitly called clone and not checkout to underline the fact that you are actually replicating all the data of the server.
If all your coders are editing files in one single directory all at the same time, well, that's pretty crazy. Not even CVS forces you to all work out of the same directory; it lets you check out your own local working copy and push changes to the server. Git is almost the same from the user's perspective, with the noted difference that you get an entire copy of the repo and not just one working copy of some of the files.
Going by the rest of this thread, I wouldn't rule out the possibility that they are doing something insane like committing multi-gigabyte objects regularly, and then only checking out with a low clone depth.
I've seen people attempt that before; without fail people who are deeply in centralized version control land and do not bother to understand git before attempting to switch to it (because it is trendy, or because people under them won't stop complaining about using svn in 2014).
[1] it is explicitly called clone and not checkout to underline the fact that you are actually replicating all the data of the server.