As a thought experiment, if you were the head of ISIS or the Russian ambassador in Washington DC, would you or would you not expect your snaps to be "really deleted" aka actually private? Honest question, not trolling.
Snapchat won't protect you from a state-level adversary, nor does it need to. It may, however, protect you from a disgruntled ex leaking your photos, or from an employer snooping on your private life. It may even protect you from yourself when you come across an old post you really didn't need to see.
Snapchat attempts to use technology to enforce the social contract of "please don't repeat everything I say to everyone you know, and don't hoard it indefinitely", which is established protocol for, say, actual in-person conversations. By implementing a casual form of endpoint security, a non-sophisticated actor at the receiving end may not break this social contract without repercussions, since nominally, only the official client can get the payload; the official client deletes the payload upon receipt, and if the official client detects that a screenshot was taken or the message was saved, it notifies the sender. That's the feature, not off-the-record messaging.
I would expect that if I were personally targeted by ie NSA, they could intercept the snaps in transit, and those copies would not be deleted. Short of that though, I certainly do believe that snaps are indeed completely deleted after they are viewed (unless the recipient makes a screenshot) because the risk to Snapchat of lying about that far, far outweighs any potential reward.
