I appreciate you responding to my criticism. The first part - there is definitely an association between believing A and believing B, but I don't think it's fair to assume B when they only talked about A.
As for what I called demagoguery: I mean, corporations are considered legal persons in most countries - that's where the word corporation comes from - which is what allows them to own property, enter into contracts, etc., as well as to violate the law. So then the US has been more uniquely inclined to allow corporations to claim rights originally intended for natural persons (such as free speech, contract rights, property rights, rights of the accused); and there is valid criticism of that idea for various reasons, the most obvious one being that they're very different from actual people, so Congress should have to explicitly decide what privileges corporations should have rather than the judicial system tacking on existing ones. But on the other hand, it's not completely ridiculous to say that since corporations and people have similar sets of abilities in the eyes of the law, the same principles should apply, especially with respect to commerce.
Even in the case of corporate free speech, there are certainly situations where governmental restrictions on a corporation's speech would feel fundamentally wrong - e.g. suppose Congress decided political activism groups, from the EFF to the NRA, were only allowed to use corporate funds to spread their message at all if Congress liked them. Citizens United, as I said, approached this in terms of freedom of association more than corporate personhood, but neither does it seem immediately absurd to try to solve it the latter way. (Incidentally, the need to find, and the partial arbitrariness of, a dividing line between that example on one hand which should have constitutional protection, and super PACs on the other which should not, is why "corporations aren't people" is a bit simplistic as an approach to solving the Citizens United problem. You really don't want to remove protection from the former.)
Anyway, it seems self-evident that corporations and individuals need at least somewhat separate treatment by tax law (e.g. because of the double taxation issue when corporations pay out earnings to shareholders). Given that corporate personhood in general is not fundamentally and irrevocably an evil or unfair idea, merely specific implementations of it, it's not fair to be reductive and say that the person analogy must be taken to absurd extremes.