<<The statement in the code that a "doctoral degree in X from a college or university approved by the Secretary" isn't inconsistent with the requirement that the degree must be from an accredited program.>>
That is correct. Here are the two statements for comparison:
1. From the U.S. Code: Applicants “must hold a doctoral degree in X from a college or university approved by the Secretary."
2. From the agency handbook: Applicants “must have a doctoral degree in X from a graduate program in X accredited by the XYZ Association.”
The first is law, the second, policy. The second is, as you say, more descriptive. It is also stricter and therefore more restrictive. The problem with the restriction is that it excludes certain well qualified individuals and all graduates of programs in foreign countries (the accrediting body only accredits U.S. programs). A colleague of mine could not work for the agency (if she wanted to) because she got her education and training in England. Excepting the agency I’m talking about, I am not aware of any agency, institution, or governing body that does not take exceptional factors into consideration via waivers, exceptions, grandfather clauses, certificates of equivalence, and so on. National security is not an issue here.
I recently described the situation by voicemail to the Director of Accreditation at XYZ Association, the accrediting body. Her voicemail reply: “Accreditation is for the program and says nothing about the individual. The remedy, if you will, for a person having been in a program that is not accredited is the ability of the individual to be licensed, which is the credential for service delivery.” Her reply will not win any awards, I know, but what she seems to be saying is that licensure implies competence, whereas accreditation does not. In others words, licensure, not accreditation, is the standard indicator of professional competence.
<< Federal law doesn't require that hiring standards or requirements "be tied to (i.e., predictive of) job performance," unless they have an adverse impact on a group or groups protected under Title VII of the Civil Rights Act.>>
No protected groups here, but if the agency’s explicit goal is to hire top performers, i.e., persons who can do A, B, and C, it has to be able to show that its hiring process selects persons who can do A, B, and C, and weeds out persons who cannot. If a variable it uses to select employees is not empirically related to the ability to do A, B, and C, how can it use that variable?
I want to thank members of this forum for their replies, and especially the person (moderator?) who re-titled the thread “Arbitrary Degree Accreditation Requirement,” because I think that precisely summarizes the issue:
Is there a problem with the accreditation requirement if it excludes eminently well qualified individuals and individuals not educated and trained in the U.S.?

