Shouldn’t Do This, but…

Just tell him you need to upgrade the outlet for some sensitive electronics and you'll pay for it. If he pushes back, tell him if it didn't matter you wouldn't be asking.

And, the NEC 240 24.b is the real deal. If he won't comply, call it in to the city. It's like gravity, it not just a good idea, it's the law. 

NEC 240 . 24 (B) says each occupant shall have ready access to all overcurrent devices supplying the occupancy 

Sounds like there might be a lot of non compliant work down there.  Are you sure the building is a legal dwelling unit?  Check with your local government.

When i owned a 2 flat my renters always had access to to breaker box in case I wasn't around to reset it for them. By right's you should have access to the electrical box in case something trips, or happens so you are able to reset the breaker.. Ask him what happens if he is not around if the a/c should trip the breaker will he always be around to reset it, plus @panzrwagn is correct it is the law to have access, unless he dosen't have it up to code and dosen't want to show it to you..I am reaching here but.... contacting the city inspector to verify your rights

is not a bad idea hope this helps

Having access to the panel, and changing electrical devices as you see fit are two different things.You have zero rights to do the latter. Contacting the electrical inspector to assert your imaginary right to do electric work in an apartment building with other tenants won't go well for you.