Under iOS 6, the screenshot feature can be disabled by developers inside their respective applications. This “feature” has been used by messaging apps, such as Snapchat, to prevent the saving of photos and other media.
Under iOS 7, it appears that the screenshot function is now enabled across all apps. It may still be possible for a clever developer to figure out a way to prohibit the screenshot functionality, but that will require an update to the app. Previously, the act of hitting both the home button and sleep/power button would immediately take away the photo view under Snapchat, but that behavior is now different under iOS 7. This has been an issue for Snapchat and similar apps in the past, so it seems likely that a solution will be found.