It's not rubbish. At the time the laws were last tightened there were serious discussion to the effect that simply being sent illegal images via email would be enough to get a conviction.
I'm not saying it's a good law.
Even if mens rea applies to this area of law, it includes categories of recklessness and negligence, which could quite easily be argued along the lines of "you were browsing an unregulated P2P network that is known for containing contraband images".
> "there were serious discussion to the effect..."
Ah, unsubstantiated claims of Internet speculation over something? That must make it true!
> I'm not saying it's a good law.
What law? Where?
> ...it includes categories of recklessness and negligence, which could quite easily be argued along the lines of "you were browsing an unregulated P2P network that is known for containing contraband images".
"You were browsing the Internet, which is unregulated and is known for containing contraband images".
In reality, you filter when you browse the Internet, and that defines your intent. The same would apply here. Access the "HN" sub-P2P-reddit for unflagged posts then nobody can claim that you had intent. If the "HN" becomes rife with unflagged contraband and you stop using it when this starts to happen as a consequence, then nobody can claim that you had intent.
If the whole network becomes unusable because it's rife with off-topic unflagged contraband, then what you really have is a different argument. You'd be claiming that the network would be unsable because of off-topic unflagged contraband. You wouldn't have any argument about the risk of criminal liability from unintended contraband download, because no law-abiding user would ever get that far.
In short: if functional network then no legitimate risk.
I'm not saying it's a good law.
Even if mens rea applies to this area of law, it includes categories of recklessness and negligence, which could quite easily be argued along the lines of "you were browsing an unregulated P2P network that is known for containing contraband images".