Was McChrystal in that position under Bush?
I don't know. But, it's not material. Gates certainly was. McChrystal, and all the CCDRs report directly to Gates. An officers authority to issue orders does not flow from the President, it flows from Congress vis-a-vis 10 USC Part II. As such, any constitutional infirmity about a sitting president has no bearing on the legal authority of subordinate officers to issue orders, so long as those orders are within the prescribed statutory authority of the officer's command.
Gates and McChrystal were clearly within their statutory authority.