Re: "Aren't they then driving without insurance?"
"I don't know about the R.O.W. but in the UK if you own a vehicle with fully comprehensive insurance you usually get what's called a third party extension, which allows you to drive pretty mutch any vehicle you are licenced for with 3rd party cover on your insurance."
No, it doesn't work that way where I live. Unless you are a motor dealer, you are insured for the car you own/ keep. Each vehicle and driver has to be specified for additional insurance on the policy.
If you drive a van, you can't transfer your insurance to a car temporarily, because more passengers can fit in a car than a van.
Being a named driver on someone else's policy does not count towards a no-claim bonus; and you can come out of a few years of 'named driver' and still be considered a first-time insured driver by a firm. This implies that the firm is more concerned about whether its premiums will get paid by the new paying customer.