So, I think you're making a mountain out of a mole hill. Get a better dictionary. And what's funny, is that after you draw an implication from the facts, you defend that libertarians don't have an obligation to be honest or straightforward. Your example is pretty bad. Most hospitals and universities ARE secular.
Libertarianism has no track record.
I do provide more than a slogan, and I do present another alternative argument as well. It was to provide an example of contract without signature, thus defeating arguments that contracts need to be signed. Your extension of it is thus wrong. I'm not making it. And at the end you as much as agree to social contract theory.