Are you sure it's that they "are" persons or just they are considered to have rights similar to the rights a person has? Seems like a pretty important distinction.
Corporations are legal persons. This is not the same a human beings which are natural persons. The defining issues in corporate law came from the anti-slavery amendments to the US constitution. All hinged around the usage of the term natural person vs the term person.
Edit: this means that the generic person covers both natural persons and legal persons
