I don't recall anything specifically in Z but RESPA states:
The lender is not permitted to require, as a condition for providing a GFE that an applicant submit supplemental documentation to verify the information provided on the application. [§1024.7(a)(5)] …such a requirement may inhibit borrowers from shopping for the best loan by leading borrowers to believe that they are committed to obtaining a loan from that loan originator… [RESPA FAQ – GFE General #31]
After the GFE has been received, the loan originator may collect additional fees needed to proceed to final underwriting for borrowers who decide to proceed with a loan from that originator. As noted, at that time, verification information or any other information could be required from the applicant, such as, bank statements and W–2 forms, to confirm representations made by the applicant in the application. [Federal Register 11-17-08, page 68212]