There is an important line in AC-120-68F (current PRIA AC) in the "Best Practices" section:

1-7 c. Disclosure. The FAA expects a pilot applicant to disclose all pilot testing failures to any potential aviation employer.

While I don't know if the FAA could take action if an applicant doesn't disclose a failure, a company certainly could deny an applicant for not living up to the "Best Practices.