Isn't a permanent resident immigrant somebody who has a green card? Surely to be considered American you need to be a citizen, which is separate from a green card.
I'm not american so very open to being wrong on this.
This hasn’t been true for a very long time (1997). I-551 Permanent Resident Cards issued since 2010 are labelled as “United States of America / Permanent Resident”, the word “alien” is not present on the document at all.