So by your logic, no one should be entitled to use the police services? If a poor person calls the police, they won't come because they know the person won't be able to compensate them for their skills? What kind of logic are you using? Sure, if you have enough money, you can always use a bodyguard or hire a private security company but for the general public, there needs to be a service available to whoever needs it. Plus, who told you that doctors should not be compensated for their skills? I never mentioned this nor implied it and I don't know why you used it in your argument.
In regards to my reference to "life" and "pursuit of happiness," that's my personal understanding and interpretation and should not affect core of the issue here. Most people are opposed to theft, for example, but their opposition can be based on Karma, higher power, morals, belief system, or simply fear of legal consequences. However, collectively, they create a large body of people who oppose theft. Likewise, many people share the belief that medicine should be a right to everyone for various reasons, and mine just happens to be the aforementioned case.