Here the Court of Appeals gives a succinct explanation of how the US legal system approaches authenticity:
Moreover, because of the procedures and processes by which our civil litigation is decided, courts are not equipped to deliver a meaningful declaration of authenticity. For such a pronouncement to have any validity in the marketplace or the art world, it would have to be supported by the level of justification sufficient to support a pronouncement by a recognized art expert with credentials in the relevant specialty. For example, in the French legal system, declarations of authenticity are reportedly made by courts, but they are based on more than a determination of which side’s expert is the more credible. In addition to the parties’ disputing experts, the French court appoints its own neutral expert who possesses the necessary expertise (see Van Kirk Reeves, Establishing Authenticity in French Law, in The Expert versus the Object, supra at 228). In contrast, in our legal system, courts have neither the education to appropriately weigh the experts’ opinions nor the authority to independently gather all available appropriate information; we can only base our conclusions on the evidence the parties choose to present to us, and our findings as to a party’s entitlement to relief are generally made according to a preponderance of the evidence standard. […]
This is not to say that courts do not address the issue of authenticity. Courts are often required to issue findings as to art works’ authenticity as an element of claims, such as those brought by dissatisfied buyers, seeking money damages from sellers or appraisers, or rescission of art sales. However, in these actions, the relief awarded by the court binds only the parties to the transaction, and does not attempt to affect the art market generally.
The whole opinion is worth reading though it does deal with a fairly specific set of issues, including the fact that the Thome suit is about a request for declaratory judgment. Although most of the cases dealing with authenticity involve artists’ foundations, there’s an even more significant law, the Visual Artist’s Rights Act, that would appear to be relevant in this case. VARA gives an artist the right to determine which works are their own.