I understand that libertarian logic uses gray areas as a means to an end of furthering their ideology, but that is not an issue for me.
Governments, as a condition of granting the privileges asscoiated with the corporate form, could specifically apply limits to its use (and should do so much more than they do, generally), but to the extent they haven't, people who control corporations don’t lose rights merely because they are acting through them.
Corporations don't have rights, because corporations don't actually exist. Corporations are treated as having rights, because they are simply vehicles for actions by natural persons, who have rights.