Im not sure I can fully agree that Harrison is "wrong". I agree he detailed more variations (which he designated type 1 - 16) than others. However I have seen examples of each of those he described, including all the versions of WWII era C Stocks (the more A1-like contoured pistol grip, the "fat" pistol grip and fat pistol grip sniper, and the contoured pistol grip sniper). I suppose the A3 handguard ring grooves I saw on the contoured pistol grip and the contoured pistol grip sniper stock that Harrison also calls WWII era stocks could have been a modification to the earlier A1 stock, but the grooves look factory cut like A3 S-stocks.
Harrison is not the only one to use the term "type". Poyer refers to "five (basic) types in variations of the M1903/1903A1/1903A3 service stock' and he refers to nineteen variations. However, in the sketch of stocks shown on page 87 it shows the "3. C-Stock" with a finger groove. I think that does indeed qualify as a MISTAKE. I dont see Harrison "in error" per se. Types, variations, versions...its all semantics. I dont see a problem with an author offering new terms to better distinguish and describe variations or versions (as long as it doesnt contradict existing verified authorities). However, it is a little frustrating that there seem to be no two sources using the same references...it does cause confusion. However, as I am aware of differences between authors, I reference the source of the term I might use for clarification and NOT because I advocate any one or another to be the one and only correct source.
Ive got Brophy's work as well, and though he has recorded reams of information not readily available today (up to 118 years after the events) his work, as an effective and accessible tool for a collector, is...challenging at best. He writes like an engineer would. I know, I am a mech design engineer and I would likely write the same way. For historical accuracy and engineering perspective, it is peerless. But it is not an easy read and I find that his work is not an effective collector's tool.