Hm. The thing we need to hammer out is the degree to which these books are self-contained magical objects, and the degree to which they are a tendril of the terror-being that they represent. The Admiral would be able to bat away incursions from enemy characters, but would allow a magical object might make its' way on board. Based on your understanding of the functioning of the books in the show, do you think that Dig could be described that way?

If that works with your interpretation of what the Leitners are, then yes, we're good with the Admiral letting Dig (and possibly a few other of the non-fatal ones) through in a combination of lax safety standards and well, how else are they going to learn.