In the middle of '42, Ordnance wanted all rifles to have pistol grip stocks. Before they had a chance to do that, A3 production started. S-type stocks were the easiest to produce, quick. With plenty of S-type stock blanks on hand, a semi-pistol grip was possible, but not the full C-stock grip.
Scant stocks (all Remington made, I believe) were only original to the M1903A4, showing up in mid to late '43. Scants found on '03 and A3 rifles were installed during rebuild or privately.