I have the owner's manuals for both of these and they do not mention the actual function of the safeties. They only say what the safety does and what it is for.

I figured that the 10/22 was supposed to be that way simply because of the way you have to take the stock off by putting the safety half way. I was quite surprised about the Rem 1300 though. It is one of the older ones before they stopped making them. Not sure if they have started making them again.