Can a dog bite through a cloth muzzle enough to draw blood?

Hi, we have an 13 year old terrier who is diabetic and blind. Recently we visited a family member with her. Also living there is a sister who has 2 large rescue dogs, both with bite histories. Their owner trains them daily. They are mostly leashed when outside, except when she is out with them.
When we arrived for the visit, both of these dogs were off leash but I didn't see their owner (she was around the corner at her car). The female dog was wearing a cloth muzzle.
I walked to the house with my dog on a leash, I noticed the female rescue dog charging up towards the porch. Since becoming blind my dog is quite nervous.
The female dog attacked my dog on the porch and she fought back but she had a large gash at the side of her neck.
The owner claims her dog couldn't have caused the bite due to the muzzle- that my dog hurt herself during the fight. My question is Can a dog bite through a cloth muzzle, enough to draw blood?
Are both dogs at fault?
Thanks!