If we're going to nitpick, then the South shooting first is as propagandistically misleading as saying Germany shot first in WWI or Japan in WWII. Yes, it's true, if you ignore the things like supplying arms to Britain or embargoing Japan or lying to the South about evacuating Ft. Sumter:

"He stated that Mr. Seward authorized him to give assurances to the Southern commissioners that Fort Sumter would be evacuated. This assurance appears to have been repeated, on various occasions, and at length with the statement that the fort would be immediately evacuated. On the seventh of April, Mr. Campbell, having learned, doubtless, that ships-of-war were in motion at New York and elsewhere, and hearing the rumors at Washington, addressed a note, indicating his uneasiness, to the Secretary of State, and received the explicit reply: "Faith as to Sumter fully kept - wait and see." On the twelfth of April, a fleet, consisting of two sloops-of-war, a steam cutter, and three steam transports appeared off Charleston harbor, and remained at anchor in the offing, inactively, during the assault which ensued. It is well known that upon the appearance of this fleet, a message was despatched to Montgomery for orders, to which the reply was, to demand the surrender of the fort, and to reduce it if compliance with the demand were refused. Upon Major Anderson's refusal, the bombardment began."