I see both sides of the issue, and if that turnout arrangement is what is available, that is just how it is at this barn. But I am a bit more in sympathy with the OP simply because it is frustrating to have to pay for damage caused by someone else’s horse. On the other hand, if the OP isn’t interested in doing extra stuff to try to prevent this other horse from ripping her blankets (which, again, I am in sympathy with- that just sucks), she may simply need to find a new barn. Neither the other HO or the BO are going to do anything, so that is one of the only other options.
One of my horses was gelded a bit late and plays REALLY rough- like a drunk frat boy. So the BO at my old barn put him out with a curmudgeon who ended up beating him up. That made my horse very defensive so his playing went from rough to nasty and dangerous. She did not communicate any of this was going on to me until he and the third horse in that field were all injured, and I really, really wish she had since I would have immediately asked for my horse to be in solo turnout (which was available at this farm). Now he is in a field by himself, which he thinks is just fine. He can’t be trusted to not play rough, but as long as he can see his girlfriends in the next field over he is a happy guy.
The point is that he is my horse and if he is doing something bad- be it blanket ripping or biting or whatever- not only do I not want to have that happen for the other horse’s sake (and its owner’s sake), I don’t want my horse to possibly be injured. I will probably never be able to have him be in anything but solo turnout, which kind of stinks, but he’s the one with the issue so I believe that it’s my responsibility to make sure it doesn’t affect anyone else.