"Corporations are people" is the plural of "a corporation is people". It has nothing to do with assigning person hood to a corporate entity. "Corporations are people" is in reference to the 1st amendment free speech rights that the _people_ who make up a corporation still maintain when they are acting as a group.
Consider not eating up the soundbites of politicians without understanding the context.
Consider not eating up the soundbites of politicians without understanding the context.