There are Remington made M1903’s, you will run across these and they are relatively rare. These were made in WW2 just prior to the M1903A3’s.
I know 03 collector’s and there are characteristics to Marine 03’s, but I don’t remember them. The Marines used 03’s early, at Guadalcanal, Wake Island, but once the Garand got into combat, it was obvious the Garand was a more advance battlerifle and you don’t see images of Marines with 03’s after Guadalcanal. There were guys who carried them later but the usage was rare.
Based only on my opinion of the steels used, the nickel steel receivers are the safest . The plain carbon steel used in the single heat treat and double heat treat receivers is a low grade material, something that is not used in rifle receivers due to a number of factors, strength and ductility being a couple of them. Regardless of the hoopla in Hatcher’s Notebook about double heat treat receivers, retaining cheap low grade plain carbon steels was a poor choice for such an expensive part. I believe the Remington receivers are even a better choice as they are either nickel steel or 8620 and Remington would have been using later forging furnaces and heat treating equipment.
Collector's prefer Springfield Armory 03's to any other maker, I don't consider RIA nickle steel inferior but SA got all the press.
If I'm not shooting, I'm reloading.