No, the United States’ policy of containment was not based on mistaken assumptions about the aims and goals of the Soviet Union. The US’s assumptions were fairly accurate.
The US policy of containment was based on the assumption that the Soviet Union wanted to spread communism as much as possible around the world. This was not really a mistaken assumption. First of all, communist ideology holds that communism will spread around the world because that is a historic inevitability. The Soviet Union had a policy of wanting to help to bring that about. Second, we can see that the Soviets actually did try to help communism spread. They were at least somewhat supportive of the communists in China. They were aggressive in forcing the countries of Eastern Europe to have communist governments. Through these actions, they made it clear that they were interested in spreading communism.
For this reason, we cannot really say that containment was based on mistaken assumptions about the Soviet Union’s aims.