It is just the subtle (actually, NOT so subtle) difference between "corporations are people" and "a corporation is A PERSON".
The former can be held to be true, and it can be proven, and the people IN that corporation do in fact, have the same rights as any natural person.
The LATTER is where we get into trouble.
Thus, corporations ARE people but A corporation is NOT A PERSON.
Again, sounds like a subtle difference, but the truth is, the difference is HUGE.
