Can my landlord claim that I was asked to leave if they did not actually ask me to leave?

I asked that they release me from my lease two months early. When I received my final bill, I noticed that the "reason for leaving" box said that I was "asked to leave due to living conditions."

Is it OK for them to do that without actually having asked me to leave?

It is not "okay." I would ask them what that means.

If you chose to fight them I would be prepared for the arrangement to be released from the lease to disappear.

How do you believe you have been damaged by this statement?

In response to Judy: I have not. My concern is that they may report this to some other organization or a future landlord, in which case there could be monetary repercussions in the future should I attempt to rent again.

You can't do anything about possible damages.

Ask why that appears on the notice. If you are unhappy, ask that it be changed. I'd keep it in writing in the event you want to do something in the future.

You can do nothing now because you have no damages.

With regard to the future: I have no intention of renting again in the next three or four years. Would any action be possible after so much time had passed?

Your damage would be by Statute by State. It really doesn't matter, though, because you don't have an action until/unless you are damaged and it sounds like that will be years from now.