That claim, however, is false and fallacious. Libertarianism is an internally consistent philosophy. It does not embrace contradictions. It's either one or the other.
So, given that the controlled-borders position and the open-borders position are opposite to each other, how do we determine which one is the true libertarian position?
There are three ways:
The most important way is to determine which position is consistent with the libertarian non-aggression principle. That's the principle that holds that it is morally wrong to initiate force against a human being.
A border is nothing more than an artificial line that delineates political jurisdictions. Sometimes it's possible to easily identify the line — for example, when a river forms the border between two states (e.g., Maryland and Virginia) or two nations (e.g., the United States and Mexico). Other times, it is impossible to see the border. Oftentimes, people cross from one state to another not realizing that they have crossed a border until they see a sign that says, "Welcome to the state of Nevada."