At some stage I assume you will need to run the cables and pipework through a hole in a wall from the condenser to the inside air conditioner. That’s normally covered over by alluminium or plasric ducting attached to the wall. You may also need a drip drain for the condenser in some cases, although sounds unlikely in your situation.
If that is the case, is that external wall common property?
If the installation effects any common property then the above will apply but I agree that its a tad excessive, especially if others have installed theirs on a wink and a nod.
Better to go along with it and get the approval as that way you won’t be threatened to have it removed if you just go ahead and put it in.
The approval can’t be unreasonably refused anyway as stated.
As an alternative, portable air conditioners are good, we had one for a while, we used it in the bedroom, did the job. You use one of them while you wait and then sell it perhaps or buy one secondhand.