As you state, the Lanchester was a "Britishized" MP28/2 and Lanchester and Sten mags are straight copies of (50 & 32rd mind you) MP28/2 magazines.
This story (usage of MP38/40 magazines) is in line with the incorrect idea of 7.62x51 Nato and 7.62x39 M.43 (and 5.56/5.45) interchangeability which is repeated by far too many soldiers and other minimally cognizant firearms users.