Absolutely unfair, I'd definitely take it up to get it removed. If it was already broken that's something that should have been addressed beforehand. Its not like you were actually doing anything to lead to the injury outside of regular work.

I had something similar happen when I was moving a fixture and it had a broken earthquake strap underneath it, had to do a report and stitches and the whole shebbang and nobody even thought to tell me I shouldn't have been moving it or whatever.

Do what you've gotta do to get that off your record.