Wise lawyers always consider both attorney-client privilege and work product protection when withholding a document or testimony. Privilege protection is absolute but fragile. Work product protection is qualified but robust. Judges sometimes short circuit the review process by examining only one of the two possible protections.
In Western Challenger, LLC v. DNV GL Group, the court held that emails plaintiff withheld from discovery deserved work product protection, so "the Court need not decide whether the emails are also subject to the attorney-client privilege." Case No. C16-0915-JCC, 2017 U.S. Dist. LEXIS 182249, at *3 (W.D. Wash. Nov. 2, 2017). If the court had stopped there, it would have left a gap in the appropriate analysis – because the defendant might later seek to overcome the qualified work product protection. But the court combined its short circuit approach with its conclusion that defendants "do not meaningfully argue" that they could overcome plaintiff's work product claim. Id. at *3 n.1.
Some courts are not as thoughtful as this. And some courts fail to analyze work product protection if they find that the privilege protects a withheld document. That approach is also frequently inappropriate, because discovery might later show that the client disclosed the withheld document to a friendly third party – which would have waived the fragile privilege protection but not the robust work product protection.