No, they didn't. Don Carlos Buell had given unauthorized verbal suggestions to Anderson when he delivered Floyd's first set of orders to Anderson earlier in December. When Buchanan learned about Floyd's earlier orders he had Floyd send additional instructions that made the orders much clearer. The book "Don Carlos Buell: Most Promising of All" by Stephen Douglas Engle explains how Anderson reacted to Buchanan's later orders transmitted by Floyd:
When Anderson received the secretary's latest words of guidance [rb: the order Buchanan told Floyd to send], he became furious. Buell's message had allowed Anderson to decide for himself when and how to act. Now the administration was drawing back.
Anderson no longer believed he had orders that allowed him to make the move to Sumter. If he thought he already had such approval, he wouldn't have wired Washington on December 22 saying:
I think that I could, however, were I to receive instructions so to do, throw my garrison into that work [Sumter], but I should have to sacrifice the greater of my stores as it is now too late to attempt their removal. [Link]
He got no such instructions. That is why Buchanan said Anderson's move was against his orders.
In his December 31 letter to Messers Barnwell, Adams, and Orr Buchanan recapped the orders given to Anderson by Buell:
"You are carefully to avoid every act which would needlessly tend to provoke aggression; and for that reason you are not, without evident and imminent necessity, to take up any position which could be construed into the assumption of a hostile attitude. But you are to hold possession of the forts in this harbor, and if attacked you are to defend yourself to the last extremity. The smallness of your force will not permit you, perhaps, to occupy more than obey of the three forts, but an attack on or attempt to take possession of either one of them will be regarded as an act of hostility, and you may then put your command into either of them which you may deem most proper to increase its power of resistance. You are also authorized to take similar defensive steps whenever you have tangible evidence of a design to proceed to a hostile act."
Buchanan continues by saying, "Under these circumstances it is clear that Major Anderson acted upon his own responsibility, and without authority, unless, indeed, he had "tangible evidence of a design to proceed to a hostile act" on the part of the authorities of South Carolina, which as not yet been alleged..."
In his January 5th letter to Colonel Cooper, the Adjutant General, Major Anderson stated, "The more I reflect upon the matter the stronger are my convictions that I was right in coming here. Whilst we were at Fort Moultrie our safety depended on their forbearance..." The fact of the matter is that while he was in Moultrie, Anderson's force was in danger. He believed, and had every reason to believe, that he had sufficient tangible evidence that hostile designs were planned against him. Nowhere in his orders are instructions to sacrifice his command; exactly the opposite. Anderson's move to Sumter was in keeping with Buchanan's instructions.