Forget TSA "requirements". It's a FEDERAL LAW to not use TSA locks. The TSA website is incorrect.
49 CFR § 1540.111 - Carriage of weapons, explosives, and incendiaries by individuals
§ 1540.111   Carriage of weapons, explosives, and incendiaries by individuals.
(a) On an individual's person or accessible property—prohibitions. Except as provided in 
paragraph (b) of this section, an  
individual may not have a weapon,  
explosive, or incendiary, on or about the  
individual's  
person or accessible property—
(1) When performance has begun of the inspection of the 
individual's  
person or accessible property before entering a  
sterile area, or before boarding an aircraft for which screening is conducted under this subchapter;
(2) When the 
individual is entering or in a  
sterile area; or
(3) When the 
individual is attempting to board or onboard an aircraft for which screening is conducted under §§ 
1544.201, 
1546.201, or 
1562.23 of this chapter.
(b) On an individual's person or accessible property—permitted carriage of a weapon. 
Paragraph (a) of this section does not apply as to carriage of firearms and other weapons if the  
individual is one of the following:
(1) Law enforcement personnel required to carry a firearm or other weapons while in the performance of law enforcement duty at the airport.
(2) An 
individual authorized to carry a weapon in accordance with 
§§ 1544.219, 1544.221, 1544.223, 1546.211, or subpart B of 
part 1562 of this chapter.
(3) An 
individual authorized to carry a weapon in a  
sterile area under a security program.
(c) In checked baggage. A 
passenger may not transport or offer for transport in  
checked baggage or in baggage carried in an inaccessible  
cargo hold under 
§ 1562.23 of this chapter:
(1) Any loaded firearm(s).
(2) Any unloaded firearm(s) unless—
(i) The 
passenger declares to the  
aircraft operator, either orally or in writing, before checking the baggage, that the  
passenger has a firearm in his or her  
bag and that it is unloaded;
(ii) The firearm is unloaded;
(iii) The firearm is carried in a hard-sided container; and
(iv) The container in which it is carried is locked, and only the passenger retains the key or combination.
(3) Any unauthorized 
explosive or incendiary.
(d) Ammunition. This section does not prohibit the carriage of 
ammunition in  
checked baggage or in the same container as a firearm. Title 
49 CFR part 175 provides additional requirements governing carriage of  
ammunition on aircraft.
[
67 FR 8353, Feb. 22, 2002, as amended at 
67 FR 41639, June 19, 2002; 
70 FR 41600, July 19, 2005; 
71 FR 30507, May 26, 2006]
Disclaimer: No law degree but I did stay at a Holiday Inn last night.