But I asked for usefulness, not just logical coherency. By that I meant useful in the context of your claim, which was that someone could believe in the Great Society programs without believing in positive rights. Not all logically coherent sets of beliefs are ones an actual person would hold as their only beliefs in the category.

For example, almost anyone will agree that it's bad to take a person's only food away. The (negative) right not to have one's property infringed on exists in the mind of any reasonable person, and they consider it to apply to that case, at least. Perhaps that right is overridden by something in some other cases, but what would you call the overriding something if not a positive right?