Help with "Flexible" vs Fixed Tables
I'd suggest you have a think about this system's use cases.  Work out in your own mind how the queries will look for the given design and for your alternative.  Include scenarios where people move between slots.  What do updates look like?  Can business constraints be enforced in DRI?  Can the desired values still be found?  Having actual examples to talk through will highlight your concerns and allow your boss to explain the model more fully.

Writing horror queries against a ghastly schema is only one part of the problem.  Someone has to fix them, at 3am, with no documentation, when they break.  More intelligible queries at this stage will give you a better system, sooner.

If it calms your nerves any, I've had success with EAV systems.  That said, we were a team of very experienced DBAs, it really was a blue-sky, "what if" project and, no, we didn't bet the company on it.  Any dev project that will be heading to production we discourage most strongly from using an EAV approach.

If you go the 'flexible' route do not try to write generic queries just because you have a generic schema.  Each query should only deal with one of Company, Location, Region or whatever your slot types are.

My two cents' worth.