I believe you are correct – See below. There isn’t an exception to the rule for appraisals. And I believe it would violate the independence criteria of the Interagency Appraisal and Evaluation Guidelines as well as safety and soundness principles to allow a borrower to select their own appraiser. From p. 77458 of the Interagency Appraisal Guidelines: Independence is compromised when a borrower recommends an appraiser or a person to perform an evaluation.
The CFPB Small Entity Compliance Guide p. 40. What charges are subject to zero
tolerance? (§ 1026.19(e)(3)(ii))
For all other charges, creditors are not permitted to charge consumers more than the amount
disclosed on the Loan Estimate under any circumstances other than changed
circumstances that permit a revised Loan Estimate, as discussed below in section 8.1.
These zero tolerance charges are:
Fees paid to the creditor, mortgage broker, or an affiliate of either
Fees paid to an unaffiliated third party if the creditor did not permit the consumer to
shop for a third party service provider for a settlement service (§ 1026.19(e)(3)(ii)(C));
Transfer taxes. (Comments 19(e)(3)(i)-1 and -4)