That's what the Leftists calling themselves liberals would have you believe. It's wrong. Socialistic so called liberals do not have those called classical liberals as ideological ancestors; the Left broke off long before the term liberal become current. The only thing giving their canard even a small bit of credibility is the fact that J.S. Mill started as a classical liberal and became a moderate socialist.
Your dichotomy is telling, though. If negative (i.e. real) liberty is libertarian and "positive liberty" is liberal, what kind of liberty do conservatives believe in?
I can see you have never actually studied the concepts of positive and negative liberty as applied to Classical Liberalism.