I suspect that the use of 'that' as a substitute in a relative clause for a personal pronoun modified by the clause was acceptable in Elizabethan England. I ran a search for 'he that' in the King James Bible and got 611 hits. For example: "He that hath ears to hear, let him hear." (Matthew 11:15, Mark 4:9, Luke 8:8)
I agree. Which, of course, is a far cry from standard English in 1972, much less military usage.
Styles come and go, and in the instance, I am quite confident of my ear. There has been a marked usage change in recent years (it always annoys me). For want of any better theory, I suspect the uneducated teachers in the public school system started teaching "that" because they themselves couldn't figure out when to use "who," and when "whom."