This is a good point, thank you. I have an intuition that while status is the ability to control the group, you can have influence without having status, although you cannot have status without having influence. That points to an flaw in my definition, one which I should resolve somehow before making that post.

I should probably note that I think that there are actually two different terms to which we refer when we say "status". Status1 (or "influence") is the ability to control the group, so it's the one I was talking about above. Status2 is stuff like official titles or other considerations that cause a situation where it's expected that people grant you Status1. I believe that people liking you would fall under Status2.