no, I don't think you should offer someone else's yarn, because if there is a problem with THAT, then you are really in a pickle.
Can you just ask him/her what they would like you to do?
Or, I guess I would ask if they minded if you tried to find the cause and try again.
Hopefully, they are nice and don't give you a hard time about what seems like a very honest mistake.
Or, maybe offer to give thier money back plus $10.00 so they can order yarn somewhere else and they won't have to pay shipping (sort of little compensation for their inconvience?)
Good Luck and let us know what happens!
my name on Ralvery is: knitnackpaddywak