“Ahem”, if CentCom had it shoved down their throat with an order to cooperate with Bremer, it was not a military decision.
Again you forget we are talking about the US military here. The US military unlike other countries are subordinate to civilian commanders.
So as you were reminded the Marines had their orders. That is their job. They are not to know or consider where their orders came from. They only need to recognize them as legal orders and they follow them.
All military decisions are based on political objectives.