I don't believe it's such a black and white issue. You have to adequately define freedom, which is basically impossible and any attempt to do so will always be ideologically driven. Besides which, what would you say to someone who lives in a totally free country, but most of the people are mired in abject poverty? What about another who lives in an authoritarian country but has all the best social services (education, opportunity for employment, health care) and a very good material life? There is no one universal edict that applies, so it's silly to issue flat generalizations like "Live Free or Die."
Yeah, this is a point that often seems to be overlooked. The way I visualize it, pretty much everyone can say "I would trade
X amount freedom for
Y amount of security." It's impossible to quantify either of those variables meaningfully, but it's just a way of representing the balance between the two ideals.
By consenting to be governed, a person is trading some of their freedoms for some of their security - I could go off and live in the wilderness with a shotgun and some basic camping gear and bow to no law but my own, but by doing that I'd be giving up all those lovely benefits of civilization that I've grown accustomed to, and of course anyone who happened to be in that same wilderness could kill or rob me and no one would do anything about it. So, for one to believe that that giving up
any liberty for
any security is wrong, that person would have to be an anarchist of some sort.
In that view, "Live free or die" is just a way of saying that a small loss of freedom must bring about a large increase of security to be worthwhile. It's a matter of where people set the limits, not so much whether they acknowledge that limits exist.
In your example, I would say that poverty results in a lack of freedom, while wealth brings freedoms of its own. Even if all people are equal before the law, money lets you do stuff that you otherwise couldn't. Of course, it's my personal belief that a smaller degree of government regulation (thus, a greater degree of "freedom") tends to make people in general more wealthy anyway.

But that's another discussion.