Not true - you can insure an untaxed car, you just can't tax a car without insurance. However, in my experience, an untaxed car generally does not have an MOT either, and probably is uninsured (they usually only try to take a policy out after they have had an accident, but we normally catch these idiots out).
Also, failing to tax a car, and then using it, also DOES NOT invalidate insurance (although I believe the fine is up to �5000 is the car is declared SORN and then driven on the road).
Sadly, the DVLA don't follow up on this a lot, despite having a grass the scumbag line on their website - equally, the police are generally not that interested as they have better things to do (eating doughnuts, pulling you for doing 32 in a 30 zone, arresting people for beating up burglars, etc, etc).