Yes, I understood that, but I disagree that it's the wrong word. It's just one of the meanings of the word "rights".

If people start getting confused, then yes, we want to use terms more carefully in order to disambiguate. We can talk about individual rights, legal or moral, positive or negative, and so on (or, as I prefer, to re-frame the question in terms of our responsibilities to one another as individuals--there is still usually a lot of confusion around even individual negative moral rights because they implicitly impose positive obligations on individuals and institutions; when talking about responsibilities the implicit becomes explicit). And we can talk about institutional power, responsibility, authority, and so on.

But they're all rights, because the word has multiple meanings.