Fischer in the Army?

Getting back to Borrowing a Chess Book, while I had Truzzi's 'Chess in Literature' on loan, I noted a curious Fischer story. The book's Introduction starts,

In 1959, while in basic training in the United States Army at Fort Jackson in South Carolina, I and another draftee were killing time in our barracks between harassments when he -- I now recall only that his last name was Schultz -- asked me if I played chess. I replied that I did, but that my game was quite poor. He told me that he had a high rating, but that playing with me would pass the time. I agreed so we played, Private Schultz devoting his more serious efforts to simultaneously writing a letter to a relative back home. [...]

About a week later, Private Schultz and I were visiting the U.S.O center. To our mutual surprise, the recently drafted chess prodigy -- and now [1974] World Champion -- Robert J. (Bobby) Fischer came in. Schultz seized the opportunity to ask Fischer for the honor of a game (rumor had it that Fischer's time in basic training was largely spent playing chess with officers at the post, so we were very surprised to see him). Fischer kindly agreed to the match while I looked on. To my amazement, Fischer proceeded to write a letter while playing Schultz in much the same manner that Schultz had done with me. And Schultz was no more offended than I had been.

Nice story, but as far as I could remember Fischer never did military service. Not being an expert on him, I turned to someone who is -- from Frank Brady's 'Profile of a Prodigy' (Dover, 1973), chapter IX, p.79:-

The question of Fischer’s potential military service was an acute one, since as a “1-A” candidate, he was scheduled to undergo his physical examination at the U.S. Army Recruiting Station on Whitehall Street in New York, and at that particular time it was believed that he might play in the Interzonal at Amsterdam [1964]. I had a few talks with Fischer on life in the military and related some of my brief experiences. Fischer is as patriotic as anyone I know but at that stage, two years in the army was the last thing he wanted.

Harold M. Phillips, past president of the U.S. Chess Federation, had been a member of a local draft board for years and I called him to see if he could suggest a way that Bobby could qualify for a temporary deferment until after the Interzonal was completed. He suggested that I contact General George B. Hershey, head of the Selective Service Bureau, and, to my surprise, Hershey was quite cooperative, though not particularly hopeful.

“A temporary deferment, on almost any grounds, is usually an easy matter to secure from a local board,” Hershey told me “but eventually Fischer will probably be drafted.” He suggested I send an appeal to Fischer’s local board and then wait until they contacted him.

There was one other way a deferment could be secured: if Bobby entered college. Alfred Landa, then Assistant to the President of the New School for Social Research assured me that Fischer would not only be allowed to matriculate into the college but he would be given a scholarship. When I relayed this to Bobby, he thought long and hard. His experience with schools was still distasteful. He negated the idea.

Eventually, Bobby took his physical examination and was rejected for reasons that have never been made public. Perhaps the local board decided that this young American would be much more valuable sitting across a chess board in the capitals of the world than he would be toting a bazooka through a Vietnamese jungle. Whatever the reason, Fischer never served in the military.

I didn't have to type that excerpt, because I found it in a Chesstalk.info forum thread titled Bobby Fischer’s 1964 Simul at Hart House, where there is an alternative reason for Fischer not being called into military service. Whatever the reason, how could Truzzi have met Fischer 'in the United States Army at Fort Jackson in South Carolina'? In 1959, Fischer would have been only 16 years old.