You said — “However, if someone sends them such a picture unsolicited and they immediately delete it, then they haven’t comitted a crime.”
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Well, I’ve heard of some law enforcement agencies scouring drives (or virtual drives) to scavenge up deleted items. If they find something that was there and deleted, I’ve heard they can charge the person. That seems sort of crazy, actually...
They'd have to be looking at a person's hard drive for a specific reason and with a warrant, like If the person was on the e-mail distribution list of a child pornographer.
Prosecutors who do this stuff are good at it- a poker buddy of mine is a Federal prosecutor who goes after child pornographers. The point he made to me is that they never find someone with just one picture or video- when they find this type of stuff after executing a search warrant, they find hundreds, if not thousands, of videos and pictures. It's tough to argue that you did not receive the stuff intentionally.
The worst is that they'll see the same child victim in pictures and videos over the course of years from a very young age to their teen years, in some cases. They just don't have any way to track the kid down. They can arrest the guys with pictures of the kids, but they can't find the victims.
It is good to be able to convict the kiddie porn collector who managed to hit delete before the police busted down the door.