Buchanan’s statement was ambiguous, and his orders gave Anderson latitude.
Anderson took advantage of the latitude to prevent his men from being shot in the back.
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.