In other words, Obama gave Cook his remedy before the Court could, thus avoiding having to reveal his BC.
I agree.
I don't think we know this for a fact, yet. If it's true (that Obama or the WH exerted influence on rescinding the order), then it will certainly come out.
It may well be that the Army treated the lawsuit as if it were a request for 'relief' from the deployment order. As I understand it, the Major was an "augmentee" to the unit being deployed, and that it is not totally unusual for such a reservist to get a deployment cancelled for hardship reasons.
There's something else that boths me. The major actually volunteered to deploy on May 8th. His orders came through about a month later. Then he sues? While he may have a legal point, this timeline is a little bit fishy.