While you'd think spraying on the rag won't get excess cleaner on the rim. It is happening where the rags moisture might get squeezed out of the rag as you rub around the spoke nipples. And that little bit that comes out will be wicked into the hole around the eyelet and/or nipple.

Do your rims get so filthy that you need anything more than a rag wet with water?

I've seen enough post here on BF and elsewhere about Simple Green and hydrogen embrittlement to make it one of my last cleaning choices to go to. Whether it's true or not, it doesn't cost me anything to avoid it.