Although the federal and most if not all state rules do not explicitly require privilege logs, all or nearly all courts demand that parties withholding protected documents describe them with specificity in a log. And all courts ultimately require parties withholding such documents to support their asserted protections' applicability – with competent evidence.
Courts disagree about when parties must present their supporting evidence. Most courts take the common sense view that parties can wait to present such evidence until the adversary challenges a withheld document's protection. This certainly saves the producing party an enormous amount of time, money and effort. But some courts are more demanding. In Pipeline Productions, Inc. v. Madison Companies, LLC, the court ominously stated that "judges in this district have repeatedly outlined the criteria a privilege log must contain" -- including "an evidentiary showing based on competent evidence" supporting (among other things) any assertion: "that the document was created under the supervision of an attorney"; "that the document was prepared in the course of adversarial litigation or in anticipation of a threat of adversarial litigation"; and "that the documents do not contain or incorporate non-privileged underlying facts." Case No. 15-4890-KHV, 2019 U.S. Dist. LEXIS 41048, at *5-6 (D. Kan. Mar. 14, 2019) (citations omitted).
Fortunately for corporate defendants legitimately withholding numerous protected documents, most courts wait to see if an adversary challenges a party's privilege or work product assertion before requiring such evidentiary support.