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1) On the vet bill, if the vet can prove they provided service and you owned the horse, then you would have to prove that the vet knew and was told that no work should be done without your approval and that they did so despite your telling them not to do any further work. If you can provide proof in court the vet was told that and that the vet knew the trainer did not have authority to authorize them to do the work, then you have a good case to get that bill vacated or dismissed. When you sue for this, if the trainer went against your orders to not get work performed without your permission, then you need to add your trainer to the suit as a third party, which would be where you bring them in the suit and state that if you are found liable to the vet for the bills the trainer is liable to you for the payment for exceeding the scope of his authority to get treatment done by the vet.
2) This second one is pretty simple, but I am afraid that it requires you to go to court against the company for violations of the FCRA in improperly reporting debt that does not belong to you. As you have already put the company on notice it was not your bill and they have violated the Fair Debt Collection Practices Act by refusing to validate the debt and are reporting a debt they cannot prove and does not belong to you, this is grounds for you to now file suit against them for damages including attorney's fees as provided for in both the FCRA and the FDCPA.
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