Go to westpoint.edu/admissions to see the process for being admitted to west point.
When I was in the Air Guard I worked with an officer who was the Admissions Liason Officer for the AF Academy. His job was to assist with answering questions for applicants for admission to the AF Acadamy. I believe the USMA has something similar.
Relative to Ben Carson, I could imagine that someone like Gen. Westmoreland could honestly say to him "you would be an excellent candidate to West Point." I think this could be inferred as an offer. However the process to gain an offer for admission would have to be initiated to start the process.