According to the timeline in this article, it looks as if Cook deliberately picked a fight. GOOD FOR HIM. If it progresses, (and I doubt Cook is going to stop) the Admin will be forced to acknowledge Obama’s legal status as a natural born citizen or not.
We'll see, there may be another shoe dropping in the near future. Like a letter to Major Cook from the Secretary of the Army thanking him for his service and then separating him from the Army Reserves.