I've had a similar issue with various guns over the years and it usually boiled down to shell head dimensions versus chamber dimensions.
Measure the unfired rim diameters and case head diameters of the Rio shells and do the same with the Remington shells. Then measure the thickness of the rims on each. My guess (and it's just a guess) is that you might have a minimum dimension chamber and the Rios are of a size that are a hair too large. Not consistently, based upon what you've said, but sporadically.
