Misunderstanding the Principle of Subsidiarity

Many conservative Catholics like to pull out the "Principle of Subsidiarity," first articulated in the Papal Encyclical Quadragessimo Anno and referred to in subsequent Papal Encyclicals on social and economic justice, as some kind of official Church policy that calls for the dismantling of the welfare state in ways that punish the poor. In essence, such folks argue that the Church position through this Subsidiarity Principle is that the welfare state diminishes the dignity and the sanctity of the individual by absolving the individual and his/her local community from conquering or overcoming the conditions which oppress him/her. To me, this sounds like the old "pull yourself up by your bootstraps" line, which is accompanied by an attitude that no one has a moral claim on the government to help one get a leg up in life when one can do it by himself and with the help of the people around him. But, while individual initiative is, indeed, to be encouraged, the social justice teaching of the Church also CLEARLY recognizes that sometimes societal and economic structures oppress and that government has a moral duty both to rectify this structural condition of oppression and to provide for the well-being of its poor and disadvantaged citizens until such structural impediments to individual self-actualization are eliminated. I admit that I do not have as much of a complete understanding of this "Principle of Subsidiarity" as it factors into the Social Justice teachings of the Church as I would like, and so I would appreciate any elaboration, clarification, or opinion on the subject that anyone more knowledgable about this subject can provide.