Often, NEMA 14-50s are not wired with a ground and the Tesla adapter doesn't use it. I had to specify a ground wire when I had a 220VAC circuit installed (not for an EV, in my shop). The electrician said "why do you want a ground wire? I never put one in." I explained that some shop equipment wants the ground and retrofitting would cost me a lot more so just do it.
Are you sure the system isn't grounded? Perhaps you are referring to the fact that the outlets don't have a ground wire. If you have a breaker panel then the odds are very high that it's grounded. If you have a fuse box, well, then maybe not. Look to see if there is a metal rod or even a wire to a metal plumbing pipe. If not, as was said earlier, grounding the system is way easy to do.
It's been standard practice since before WWII but running a ground wire has only been standard practice for the last 30-40 years. I have an old house that has wiring dating back to the 20s and it's well grounded though some of the circuits don't run ground wires.
Depending on your relationship with the landlord, you might be able to get them to pay for the fix. They are assuming a lot of risk by having a completely ungrounded system.