No, your understanding is not correct. I'm just not worried about *possible* secondary motivations right now. She seems very involved for someone with no "skin in the game". I believe that there's a good possibility she is trying to actually solve the healthcare problem. Sometimes, the best solution isn't the one presented first. Hurried solutions are almost always the wrong solution. Finally, solutions for all American's that ignore the people representing a significant number of Americans shouldn't be a solution we embrace. That's part of why we are still talking about healthcare 8 years later. Lets fix it right and be done with it.
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You are right though, people are "more likely to give away the peoples money" when its not their money. Also, people are more likely to look at it more objectively when they have no personal interest. In my opinion, it's too early to determine her real motives, I'm choosing to show some optimism, there's plenty of time for pessimism later.