§ 91.9 Civil aircraft flight manual, marking, and placard requirements.
(a) Except as provided in paragraph (d) of this section, no person may operate a civil aircraft without complying with the operating limitations specified in the approved Airplane or Rotorcraft Flight Manual, markings, and placards, or as otherwise prescribed by the certificating authority of the country of registry.
(b) No person may operate a U.S.-registered civil aircraft -
(1) For which an Airplane or Rotorcraft Flight Manual is required by § 21.5 of this chapter unless there is available in the aircraft a current, approved Airplane or Rotorcraft Flight Manual or the manual provided for in § 121.141(b);
Failure to meet all the airworthiness requirements of the aircraft, very much to include all relevant documents and paperwork, means the aircraft is unairworthy and not in compliance with the regulation. Flying the aircraft means you are flying an aircraft without a valid airworthiness certificate (see line 6 of your airworthiness certificate, on the certificate itself).
The regulation has nothing to do with the PIC, insofar as making the aircraft unairworthy. The aircraft in this condition is unairworthy with or without the presence or input of the pilot in command.
The pilot in command who flies this aircraft in an unairworthy condition is in violation of 14 CFR 91.7(a):
§ 91.7 Civil aircraft airworthiness.
(a) No person may operate a civil aircraft unless it is in an airworthy condition.
§ 3.5 Statements about products, parts, appliances and materials.
(a) Definitions. The following terms will have the stated meanings when used in this section:
Airworthy means the aircraft conforms to its type design and is in a condition for safe operation.
In order to be considered airworthy, two points of consideration must be met. The item must be safe, and it must meet approved data and documentation, including type certification. Part of the type certified product in the aircraft is the aircraft flight manual, as it contains aircraft specific information, and the manual is an FAA approved document specifically assigned to that aircraft. Lacking a complete and current manual means the manual is not in compliance with the regulation, and the aircraft lacking that complying document is not in compliance, and is therefore, unairworthy.