Re: All These Cameras Photographing Cameras...
Android does, on hard keys.
It's usually either Power + Home or Power + Volume Down.
However, it is possible for an app (or GUI element) to tell the OS that it would prefer not to be involved in screenshots.
This is really useful on desktop OS because it's easy to forget that you've got Sekrit Fing half-visible when taking a screenshot of Public Thing, and it's nice if it automatically hides itself.
It's not security though. It's only a defence against accidental screenshots, not intentional ones.