When I was in high school, I was INFOEMALLY told by Naval Academy representatives that I could have an appointment if I wanted one. That would approximately be an informal offer of a full scholarship, as that is part of the package. I never applied. I never received an appointment. Nonetheless, an informal offer was made.
But Carson never said an informal offer was made.
He said he had "dinner" with the general, which didn't happen. At best, it was a buffet with a hundred or more people that occurred on an entirely different date than the one he claimed it happened on.
He makes it sound like it was a private dinner, "and that later I was offered a full scholarship for West Point." The way that sounds, it's like he got a formal letter from West Point seeking him out!
At best, what really happened was he might have met the general in passing (if at all), who encouraged a bunch of smart kids to apply to West Point and receive a "full scholarship," since everybody who is accepted receives that said scholarship, though they have to serve 4 years to pay it back!