Most rental insurance also excludes negligence claims among other claims.
I'd put in writing to the rental office exactly what I was getting and where it was going and then get a written response,
Hello; To the OP, We are not trying to rain on your parade. I am not wanting to stop you having a big tank.
If you can pay the freight for all possible damage out of pocket that is one thing. Even if you have the money it will still be cheaper to get the proper insurance with a rider in writing about the big tank.
Having permission in writing from the apartment manager/owner(s) is sound. Be sure the size of the tank is mentioned.
Get it in writing with the size of the tank or tanks mentioned.
Bear in mind you will be liable for damages of the renters/owners of any other apartments that happen to get flooded or some other damage in addition to the potential damage to the building. You may have to stand good for their expenses such as paying for another place to live while their apartment is bein repaired.
There is a very real possibility full disclosure will 1) wind up having the apartment people say no. There is also the possibility that it will be difficult to get the proper insurance. These things may nix your having the tank at all. Might be time to move.
I rented for a lot of years and finally got my own place seven years ago. I can do what ever I want. Interesting thing is I think more than twice about potential about damage to this place.