The only plausible reason I can think of for this approach, is that the people involved aren't comfortable with makefiles, and don't want to admit weakness. There are plenty of folk spoiled by IDEs in this camp.
If you pull in all your .c files via #includes, what this buys you is that you can use a single makefile, never have to add new modules to it.
On the downside, you completely screw your namespace; you can't use private variables or private helper functions - everything is effectively global.
And the compile time will be horrible, of course.
Anyway, my advice to you is:
1. avoid being confrontational; for better or worse, you have to work with these guys
2. stick with objective arguments (i.e. total compile time, namespace issues); anything resembling a religious argument will get you shut down
3. if at all possible, show proof of concept of something better, and do it in your own time