Pursuant to the Presentment Clause, a Congressional Act is signed into law by the President and then transferred to the Archivist of the US as evidence of US law. All evidence of US law is held in trust by the Archivist of the United States. The Archivist is appointed by the President. An ineligible President invalidates appointments made pursuant to the Appointments Clause. Evidence of law held in trust by an Archivist appointed by an ineligible President puts the Judiciary Act, as amended, in jeopardy.
The Judiciary Act provides authority for the District Court to operate. The Act established a circuit court and the district courts in each judicial district. An ineligible President voids the authority of the district court and ultimately the U.S. Constitution. The courts are avoiding eligibility challenges to preserve the status quo with disregard for their oaths to support the U.S. Constitution pursuant to Article VI.
You’ve forgotten that the appointment of David Ferriero as Archivist of the United States had to be confirmed by the United States Senate under Advice and Consent consistent with Article II, Section 2, paragraph 2.
A nominee is just a nominee until they pass confirmation.