I was about to post something similar, I think the end goal is for Facebook to start selling automated comment moderation as a service, probably via some sort of wordpress like plug in.
By increasing the liability for sites without automated moderation they practically force sites to buy automated moderation, which Facebook conveniently starts selling, so the law generates them a huge locked-in market.
As a matter of subjective opinion you're completely right about people blindly believing things that are wildly untrue. However as a matter of law (and IANAL) the standard is something like a reasonable person knowing the totality of the facts (or circumstances or something). This is a much higher standard and makes convicting her of defamation a much harder push. I don't know if evidence that many people did believe something affects the courts calculation at all, my suspicion is that it does not.
Are they serious about accessing the site being illegal? When I read it I simultaneously thought that it was incredibly unlikely because of the generally bad understanding of technology on display, and at the same time incredibly likely because making merely accessing certain sites is illegal sounds like exactly the sort of thing the Tories would do.