I really don't even understand how people come for conclusions like this, how is the leader of the freeworld a puppet which is controlled by somoene else? Makes no sense to me personally.
Many politicians are subject to pressure from special interest groups. Special interest groups (effectively) contribute to politicians campaigns on an ongoing basis, and politicians want this support to continue. Also, many politicians move on to be lobbyists after leaving office, and they want to stay in the good graces of those they want to eventually work for.
It is a far stretch for the president to be controlled by a single group, however I would not be surprised if many lower level politicians are (nearly) controlled by a single person/group/organization ("third party"), however each third party likely controls very few politicians.
