Reagan as much directly contributed to the tearing down of the wall as Kennedy was a true Berliner.
Sorry, but he is massively overstimated, because he made his people feel good with his low sounding voice of his, you see.
The wall was not teared down by either Reagan or Gobatchev or the Westgermans. It were the Eastgermans. Reagan did not much to help it and official Us policy did not want it, Gorbatchev did not want it happening, but refused to prevent it by force.
France did not want it. England did not want it. Westergermany did not expect it either (but always said that it was the goal of inner-German politics). The only ones who both wanted it and pushed for it, were the Eastgerman people. They did the deeds, they took the risks.
They just had simply enough of it, and history opened the window of opportunity by having put a relative "philantropist" in charge of the Kreml. What, regarding these events, cannot be said of Thatcher, Bush and Mitterand. If it would have gone according to them in Octobre, Novembre 1989, the Eastgermans would still live in tyranny.