They're wrong.
As a general rule, insurers who write off cars in A and B class do so because the car is pretty much a mess, and you simply wouldn't want to spend that much putting back on the road. Their own 'rules' state (as per your link) that the cars cannot be put back on the road, however as the owner of the car you can do what you want with it.
http://en.m.wikipedia.org/wiki/Car_check
The wiki explains it pretty well. As long as it passes MOT and the VIC, then you're good to go. How am I so certain on this? Because I was proved wrong by a mate who bought a Cat B MX5 off Driftworks, and is driving it perfectly legally. It should never have been a Cat B in the first place, but the insurer classed it as that. When I'm wrong about something, I tend to make sure it never happens again!
So yeah, you can put anything back on the road, if you can be bothered to do so.