...relying on social media for information in a more immediate form that radio and TV can't offer. Switching off social networking would deprive us all of such a lifeline - and therefore create greater fear.
Indeed, in the last week social media has really proved itself as a force for good, as one Twitterer sagely pointed out: "Urban rioting existed before SMS/social media. You know what didn't? Large-scale community cleanups spontaneously organized within hours."
It's hard to see how any government - even if it had real-time access to social network data - could do much about disrupting riot plans as they were happening.
And, of course, it would be easy for would-be plotters to move to another, unregulated and unmonitored network if they thought their network of choice was being accessed by the police.
It's unlikely that the Prime Minister's comments will be translated into action anytime soon, however. Getting the government to understand the real impact and implications of social networks - and then act upon them - is improbable.
But there is a bigger issue here, too. We all need to understand the consequences of the huge amounts of data we are dumping into these social networking sites.
We all devote huge amounts of time to developing and maintaining our social networks, because we benefit from being more connected as a result. But, just as that information that we freely give is very useful to marketers, imagine how useful it could be to a future, less benign, government, if given enough access and enough processing power - neither of which it is likely to get.
Imagine if that government decided to block everyone who was poor, or who lived in a particular area, or who was friends with a particular person, from using a social network in a time of strife.
From one perspective that would be an incredibly effective way of shutting down any potential trouble, and from another perspective an incredible demolition of our rights.
It might be a far-fetched situation right now for sure, but we must always be careful whenever we give the government any new powers over us - and our data.
Steve Ranger is the editor of silicon.com and has been writing about the impact of technology on people, culture and business for over a decade.
Steve Ranger is the UK editor of TechRepublic, and has been writing about the impact of technology on people, business and culture for more than a decade. Before joining TechRepublic he was the editor of silicon.com.