Fleet boats did indeed carry 22 (eg. Sargo class) or 24 torpedoes (Gato and models after that). No point having a big boat, with 10,000+ nm range and many weeks endurance if it could not carry the reloads to take advantage of the sea time. Actually, early fleet boats like the Sargo class carried 4 of their reloads externally, but that was discontinued in the war. So the game is incorrect for the wartime Sargo class, as they should only have 20, not 22 (that is there should be only 12 internal reloads, not 14, as modeled). Gato and up are correct at 10 in the tubes, and 14 reloads internally.
P.S. one of my favorite sites for US Sub information and pics:
http://www.navsource.org/archives/subidx.htm