Etymology and meaning of "navy file"?
Solution 1:
It most likely refers specifically to enlisted Navy personnel as opposed to officers, as in rank and file.
Solution 2:
This is why you don't stop at the first dictionary entry for a word.
file 2
noun
a line of people or things one behind another: Plains Cree warriors riding in file down the slopes. • Military a small detachment of troops: a file of English soldiers had ridden out from Perth.
As you can see, the second entry here refers to a small group, or detachment of troops. It could also be used figuratively, especially as a synecdoche.