Yes, it sounds to me like a genuine mistake and I am sure the groomer, if she is a good one as she sounds to be, is probably feeling mortified by her error. I would definitely go back, especially as she has been so apologetic, offered free work etc. Give her the chance to make up for her error. Getting - and keeping - a good reputation is hard work, and as she can't work miracles and stick the fur back on, she is doing her best to make up for what has happened. Give her the benefit of the doubt.