Why is it that sealed arrest records are not actually sealed?
Why there isn't a proper threshold cryptosystem and chain of custody of keys for sealed records? Well, that's a different question. The answer is probably along the lines of "the justice system doesn't get tech" or "the people who could demand this don't know about it or don't care enough" or even "thus far the implementation has worked ok...".
But you don't want that stuff sitting in a court record that anyone can walk in off the street and ask to see. So part of the record get sealed - not available to the public. It's still available to the judge, and to the (outside) counsel for the other side, and to the appeals judge if things go that far.
And only certain details get protected. One side has to ask for it, and the other side can protest, and the judge has to weigh the protection for the side that wants it sealed against the interest of the public to know what went on. More, a redacted version is (usually?) released eventually.
That said, someone in the military looked over the case and oked your friend. Someone knew. A judge cannot force the army to take someone they don't want, nor hide information from them. The army is also not a dumping ground for criminals. Someone saw value in your friend, something that the military could use. He probably did well. Most young recruits from such alternative enlistment paths work out great.