In studing a map, the eastern end of Sullivan Island would have been easier to have landed reenforcements and supplies on than trying to run a ship like the "Star of the West" into Charleston Harbor to unload supplies at Fort Sumter. It looks like Fort Moultrie would have covered the shipping channel as well as Fort Sumter. Without a demonstrated threat from the people of Charleston it would seem that Anderson acted without provocation. Highly uncharactoristic of a professional army officer, almost bordering on cowardice.
While I don't know if it can be proven, it would seem that this move would have been a lot of responcibility to take on for a mear Major to be acting alone without some sort of political backing, especially if he were acting against orders in moving his garrison.