There's actually a big debate between math educators on whether abstract algebra courses should follow a groups first or a rings first approach so it is totally possible to teach rings without appealing to groups. (I'd still argue that both approaches have their advantages and disadvantages and that there can be value in using groups to teach rings though, I just wanted to say it's not as obvious as you might think)

I could be wrong here, but my read of that comment is that they're talking about the structural differences between rings and groups at the research level. Which I guess makes sense, since you're in very different territories if you're talking about something like representation theory of finite groups...

Otherwise I agree with you, there's a lot of pedagogical value in combining coverage of algebraic structures.

Yes obviously you need to know what a group is to even begin ring theory but ring theory looks and feels nothing like group theory.