Developers of these types of apps can't necessarily prevent a screenshot from happening but you they can at least notify the user who sent the content that a screenshot was taken, which in turn lets them know not to trust the receiver.
Which is why I find this stuff sort of funny.
My camera says otherwise.
Why, because they are being held accountable for something they said?
http://www.vice.com/en_ca/read/cowards-are-blackmailing-youn...
Its an issue of protecting users who are using apps like these believing their privacy is safeguarded.
Whether this problem can be fixed with a technological solution, rather than a more dramatic social change, is doubtful, but since the can of worms has been opened, its worth trying.
No, it's not worth trying, because a) it won't work, and b) it will have unintended consequences.