there has to be more important things in your life than to worry about that mirror. If there isn't, find some
The worst that might happen is they charge you for it. If they try, personally, I would at least try the argument that their placement of the machine is the actual cause, not your actions.
then if they really want to push it, try negotiating. I would start with;
No way in hell, it was your fault, not mine. You should be offering me free membership for years to come.
all the way up to;
how often do you want me to pick up the towels in the shower room.
Just relax. Life is tough enough on it's own. Worry about things that matter and that you can have an effect on.
this isn't either one let alone both.