How Independent is "Independent"?

I have a question that has long been on my mind: is a "self-identified independent" who votes in the Democratic Primary really an "independent" in the sense that they aren't affliated with either party? Given that they have chosen to activity participate in Democratic Party event, indeed in American politics really the only mass-level party activities we have are the primaries, haven't they essentially declared their "Democrat-ness" for the moment?

I understand that for the purposes of interpreting poll data that such self-identification by respodents can be useful, but the idea that someone who has consciously decided to participate in the Democratic Party's nomination process is independent in the sense that that person really is detacted from the broader partisan framework is wholly incorrect (or so it seems to me--it is certainly semantically problematic).

A person who votes in a Democratic Primary is a Democrat in the only empirical way we can measure party membership: participating in a party candidate selection process.

Really what analysts are trying to say that they believe that self-identified independents voting in the primary tells us something about "independents" who are not voting in the primary, but may vote in the general election. A better question to ask, it would seem to me, is not whether someone considers themselves "independent" but rather whether they voted Democratic or Republican in the last several elections. If they truly vacililate, then perhaps defining themselves as "independent" makes sense. If they normally vote Democratic (or Republican) then that tells us something that self-categorization as "independent" doesn't.