While I do think that is the general rule since humans are social animals, I'm curious as to why you don't think there are exceptions. By definition, to chase status means to pursue things that society values. It seems to me there are certain people who do not chase such things because they have value systems that don't align with the society they are a part of. Perhaps I can agree if we lax the assumption on what defines a society. If your family or a church is sufficient as a "society" I could agree, but I was using a larger definition to include people one wouldn't know on a personal level.
>status has more degrees of freedom than the number of people.
I don't know if I'd go this far. Status is by definition relative social standing and thus defined by the society at large. It can be relative between cultures (some societies may give teachers more status than lawyers and vice versa) but it can't really be relative within a culture and still meet that definition of aggregate consensus. Naturally, within cultures some dimensions will be more valued than others as the ones that give prestige.