You should also note from Decision 13-2/1.1, "When fairly taking his stance the player is required to take his stance in the least intrusive manner that results in the minimum improvement in the position or lie of the ball, area of intended stance or swing or line of play." (my emphasis)
The Rules permit a player to "fairly take his stance", but this does not include the right to "back in" unequivocally. You need to read Decision 13-2/1 (too long to post) to fully understand the limitations.
At the US Open, every group has a walking referee accompanying them to assist the group with the Rules and prevent breaches. Obviously, it was the referee who concluded the ball(s) must be dropped rather than placed (because the exact spot or precise lie was not known sufficiently).
The stick is a loose impediment (see Rule 23). As I see it, you had three options:
1. play the ball as it lies.
2. remove the loose impediment. If the ball moves as a result, it's a one stroke penalty and the ball must be replaced.
3. deem your ball unplayable and proceed under one of the options of Rule 28, with a one stroke penalty.