One reason I believe free-will cannot be assumed to be libertarian free-will is the forum in which this thread is posted (Calvinism vs Arminianism).
Arminianism obviously does not advocate libertarian free-will. Instead it maintains human free agency exists throughout salvation (man is influenced by the flesh and by the Spirit).
@DaveXR650 brings up like pertaining free-will, and it is certainly true that some within free-will theology (not Arminianism) believe that man can, of his own uninfluenced nature, choose God.
Among this minority sect some still leave room for divine influence in terms of man retaining an element of God's image in their nature (that natural man innately struggles between right and wrong, between two opposing desires).
Søren Kierkegaard famously discussed this in Purity of Heart is to Will One Thing.