Found this, FWIW:
14 CFR § 61.59 - Falsification, reproduction, or alteration of applications, certificates, logbooks, reports, or records
(a) No
person may make or cause to be made:
(1) Any fraudulent or intentionally false statement on any application for a certificate,
rating, authorization, or duplicate thereof, issued under this part;
(2) Any fraudulent or intentionally false entry in any logbook, record, or report that is required to be kept, made, or used to show compliance with any requirement for the issuance or exercise of the privileges of any certificate,
rating, or authorization under this part;
(3) Any reproduction for fraudulent purpose of any certificate,
rating, or authorization, under this part; or
(4) Any alteration of any certificate,
rating, or authorization under this part.
(b) The commission of an act prohibited under
paragraph (a) of this section is a basis for suspending or revoking any airman certificate,
rating, or authorization held by that
person.
Seems that Para (a)(2) could be a problem...