You've put your finger on one of the many good reasons that a strong and open channel of communication is essential with the coaches who are making offers. Their insight into a recruit's admissions prospects are essential to the decision; and, as TPM indicates, they will often be in close communication with their admissions office to have the best possible feel for those prospects.
Often, the Head Coach and/or the Recruiting Coordinator will be confident of a recruit's standing to give the player and his parents enough confidence that they decide they can accept the offer. At other times, the coaches have to return from their conversation with admissions with a view that inspires less confidence. It depends on the school, the player's credentials, and the strength of the communication lines.
One more, related thought: All offers are conditioned upon a player's satisfactory completion of his senior year of high school. All of us who have been observing this process for some time can relate horror stories about players who slacked off in the classroom after accepting their commitment and found themselves in a real jam coming out of high school. Believe me, you don't want to be in that position.