how does a lender ensure a perfected security interest in a registered copyright?

Yes it seems to be true. Two decisions from the federal courts in CA In re Peregrine Entertainment, Ltd., 161 B.R. 194 (C.D. Cal. 1990) and In re AEG Acquisition Corp., 127 B.R. 34 (Bankr. C.D. Cal. 1991), aff'd, 161 B.R. 50 (Bankr. 9th Cir. 1993), have held that a security interest in copyrights or rights under copyright must be recorded in the Copyright Office in order to perfect the lien. Parallel UCC filings were held to be ineffective. These courts noted that the Copyright Act, 17 U.S.C. § 205, contains comprehensive provisions for recording security interests, and held that these provisions preempted state UCC methods of perfecting security interests.

But since UCC filings are done against the debtor, the lender needs to be sure of the exact title or registration number of the registered work to record a copyright lien.

This can be tricky, so you're best off hiring a lawyer for help.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.

Copyright and Patents are strictly federal creatures in nature.
All liens must be place with the US Copyright office www.copyright.gov.
Even if a contract is state, when it contains a Copyright clause, then a dispute about that clause is a federal question.