Who is responsible for an accidental mess by a two year old?

While visiting a friend my daughter got diarrhea. She came up to me while my friend was showing me her daughter's finished nursery and asked me where the bathroom was. I looked down at her and was about to tell her when I noticed it all down her legs. She has been potty trained for over a year and wouldn't just do something like that. I took her to the bathroom and started cleaning her up while my friend got her kids and locked them in the living room and started cleaning up the mess. She was crying hysterically, saying uncalled things, and had her husband get on the phone and try to get ahold of someone right away to come out and clean her carpets. My daughter only left two spots from what I saw. One in the bedroom where it happened and one where she stopped to ask me where the bathroom was. I ended up crying because I felt so bad and helpless. My daughter was gagging and was also very upset. When I was done cleaning my daughter I asked her if there was anything I could do and she threw up her hands and shook her head. I said I was very sorry and for her to call me later. I didn't know what to do. I didn't want someone acting like that around my child nor did I want her to get her kids sick if she were sick. When I got my daughter into my truck she told me she was sorry and it was all her fault. I don't think a 2 yr. old should feel that way, it was only an accident. Well days p and I hear nothing from her. I texted her and told her I was very sorry and I hope she didnt hate me or my child. I got no response. Days go by and I get an email from her with the carpet cleaning bill. $150 telling me I needed to pay for the damages my child created in their home. The bill says that the bedrooms, hall, and living room were cleaned and removale of feces as well as a late night service fee. Her email said I was taking food out of her kids mouths and I was not being a friend if I didn't pay this. I have my own carpet cleaner and would've been more then happy to bring it over and get the mess up but when I was done cleaning my daughter they made it aparent they were going to do what they were going to do and I could've been of no help. I never agreed to this nor do I think I should have to pay for someone to have their carpets cleaned because I wasn't even there to see what was cleaned. It wasn't discussed. But because I don't feel I should pay anything nor do I have the funds just to hand someone for this they are threatning me to take me to court. What should I do and what can I do??