This is what the APA actually says:
To the extent necessary to decision and when presented, the reviewing court shall decide all relevant questions of law, interpret constitutional and statutory provisions, and determine the meaning or applicability of the terms of an agency action. The reviewing court shall—(1) compel agency action unlawfully withheld or unreasonably delayed; and
(2) hold unlawful and set aside agency action, findings, and conclusions found to be—(A) arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with law;
(B) contrary to constitutional right, power, privilege, or immunity;
(C) in excess of statutory jurisdiction, authority, or limitations, or short of statutory right;
(D) without observance of procedure required by law;
(E) unsupported by substantial evidence in a case subject to sections 556 and 557 of this title or otherwise reviewed on the record of an agency hearing provided by statute; or
(F) unwarranted by the facts to the extent that the facts are subject to trial de novo by the reviewing court.
In making the foregoing determinations, the court shall review the whole record or those parts of it cited by a party, and due account shall be taken of the rule of prejudicial error.
So, it appear that years of using the shorthand "arbitrary and capricious" to designate the APA standard of review is dangerous. UPS would have been successful had it been able to show that Customs' determination was "not in accordance with law" or "in excess of statutory . . . authority."
And how would the Court decide if Customs had acted in violation of the statute? It would interpret the statute using Chevron deference to figure out what the statute means. Which is what Judge Carman did. Chevron applies rather than Skidmore because there was a regulation in play although Customs also cited guidelines and other less formal rules.
I admit I went astray. I'm glad Judge DiCarlo did not get a chance to see this.
Apparently I needed two sentences saying, "Because the statute, as interpreted with due deference to Customs, provides authority for Customs' actions, the determination is in accordance with law and not in excess of statutory authority. Thus, Customs' determination is consistent with the Administrative Procedure Act."