She can list anyone she wants. However, her telling the medical provider that your husband is financially responsible is pretty much worthless for the medical provider. Absent a contract in which he agrees to be liable for the bill the provider would lose in court suing him for payment of the bills. But if he wants to fix getting the bills and phone calls collecting for this he will need to go to court to do it. His view that the court will always side with the ex is not only not correct but is self-defeating. He has no chance to change it if he doesn’t even try. He needs to get the backbone to challenge her and make sure she pays what the order says she is liable to pay.

By the way, the allergy clinic very likely violated federal law in disclosing your step-son's medical information to you. Although you may not like hearing this, since you are not his mother you should stay out of this sort of thing. It will only inflame the ex and make things even harder. Your husband is the father, and it's up to him to deal with things like the medical needs of his kid. I know you probably just want to help your husband out, but I've seen too many situations in which the “helpful” step-parent oversteps his/her role and makes the relationships involved worse rather than better to know that it doesn’t often work out well.