Tapping the green checkmark isn't enough permission?

Playing the Devil's advocate (IANOCoder), but perhaps the bulk of the 1s&0s are being uploaded and then decrypted by sending a small string when the user selects "publish"?

Probably not.

That's a little silly. How is trusting them to correctly implement an encryption scheme terribly different from trusting them to responsibly delete aborted photos in the first place?

That would be the responsible way to do it, surely, although they should still mention it in the TOS.