That's a silly hand-wavy thing to say that doesn't reflect how Snapchat is actually used.

Although it's trivial to take a screenshot, the sender receives an alert telling them which friend took it. Given snapchat is used for sharing pictures with your close friends, that puts having your Snapchat made public in the same probability range as having your mobile phone hacked and pictures posted online. Sure, it happens, but that's a risk people are obviously willing to take.

Snapchat provides a mechanism for trusting your friends now without needing to trust them for infinity.