@JustDoingMeYour last post, I'm curious as to whether you are intentionally posting a missed insight for Carla, as she is observing Harper. Don't get me wrong, his rant does drop a hint or two, but it wouldn't indicate a person that had never been in the military. The point that you made specifically was his use of "Food Chain", which yes, does indicate chain of command. While tiny bits of colorful jargon such as this can vary from branch to branch (and even unit to unit), it is never used in an official capacity. Of course, I am using United States military jargon, as non branch-specific as I can (considering my own history).
A specific food chain, as indicated by the use of the word "my" tends to indicate a direct line rather than a general indication of position within ranks on the grander scale. I.E. the Captain of a refueling station would still be higher than Harper on
the food chain, but would would not be within
his food chain, as he is not assigned under the station Captain directly.
Now, as he is dropping it in conversation lightly, it could indicate the possibility of a history as an NCO prior to becoming a Lieutenant, which would add up considering his age. It might also indicate that he's trying to catch whether or not Carla has a military background, dropping subtle bits like that. Either way (or both, depending), he does have a working history with the Alliance Military.
Oh the other hand, if Carla is making an incorrect assumption based on a miscalculation of the scene, for the sake of dramatic tension and/or an interesting scene later, awesome. Otherwise, he hasn't really done anything out of character for a newly assigned officer.