May be one of the most overstated, unsubstantiated claim about the Reagan legacy. The USSR collapsed due to the failure of the communist system...Reagan just happened to be in office as it melted down.
The cold war was a conflict between two economic systems.
Reagan used ours to crush theirs.
It was masterful.
It was centerpiece to his efforts.
It is a significant component of his legacy.
Reagan laid it out as a goal when he entered office.
He pushed the country toward that end. He succeeded in ways unimaginable at the time. Then he rubbed the USSR's Communist noses in it with his Berlin Speech.
Kind of like saying Napoleon's armies collapsed due to the failure of the French system...Wellington had nothing to do with it, he just happened to be in Waterloo at the time.