It seems at least currently one can apply without being nominated.
My father went to West Point, and as I understand it he was given financial help since he couldn't otherwise afford it. Although my knowledge of this is based second hand on conversation I had with him decades ago. Sometimes such impressions are in error.
That may well be true. I am not an expert on how admissions are CURRENTLY handled by West Point.
I can only speak of the process my brother went through during the time
fame Carson says he was “offered” a scholarship to West Point.
I am sure my brother had to apply too, before he was nominated by
a U.S. Senator. But I am certain the process is the same.
You apply. You are either nominated or not nominated and finally you are
either appointed or not appointed.
However, there is no such thing as being “offered” a scholarship.