As far as whether you are "legally bound to pay" I can't answer that because I don't know all of your facts and can't evaluate your case.
I am guessing, and please let me know if I am wrong, that you believe because the bank resolved the issue in your favor then you may think that means you are not liable. However, that assumption is incorrect.
I can tell you that just because the bank sided with you in the dispute doesn't mean that you aren't liable for the debt. You could still be liable, you could even still be sued and a court could find that you are liable if the facts support that decision.
As to how to keep it from affecting your score you can sue them to have the court declare that you are not liable and then that court order would resolve the issue. If a court says that you are not liable then you are not liable and you can use that court's judgment to insist that the credit reporting agency or agencies remove any negative info about this account from your listing.
The lawsuit is the ONLY way to make sure that the claim doesn't affect your credit.
Short of that you could hire a lawyer to write them a threatening letter explaining how you aren't liable and that if anything negative is placed on your credit report that they will be sued under the federal and state Fair Credit Reporting Acts.
If your question has been answered then I'd offer my best wishes to you and ask that you please not forget to leave a Positive Rating so I receive credit for my work.
Of course, please feel free to ask any follow up questions in this thread. I want to be sure that all of your questions are answered. In addition, once you issue your Positive Rating the question will lock open and no longer time out so you can come back to it anytime in the future if you think of any follow ups.