The mistake is to assume that their main differentiator is secrecy or privacy. It isn't. It's convenience, immediacy, ephemerality and its effect on how you communicate, and one-to-one direct visual communication—in that order, in combination. It's the experience, not the immaterial promises they make.
Privacy was always an empty promise, and it never mattered to the vast majority of their users.
Ephemerality doesn't truly exist without secrecy and privacy in this case. It's one reason I don't use snapchat, because the "experience" is misleading.
It does, in fact, exist. The experience of ephemerality is all that's necessary, and the experience is that you take a photo, it exists for 10 seconds for all intents and purposes users care about, and then disappears. Disappears here means that I, my friends, and people I care about ever see it again. They don't, I don't, so I'm happy.
Remember, you are not their target market. Their target market is 2% people like you (nerds concerned about privacy and indirect/intangible principles) and 98% people who just want the experience.
I still think those 98% would be upset to know that someone somewhere still has access to those photos. It would certainly change the behavior of a huge chunk of them w.r.t. the service.
Privacy was always an empty promise, and it never mattered to the vast majority of their users.