it depends on what the insurance policy states, fully comprehensive doesnt mean any driver - it just means that should you crash they will pay for repairs to your car.
It would be rare for a policy to allow ANY driver unless you had specifically asked and paid for it.
However should the policy say any driver then no the other person doesnt need their own policy
the any person insurance policies are usually for company vehicles, and often have further stipulations, such as 'anyone over 25' or having held a licence for 3 years etc. For these policies, like danny says, the driver does not need to be insured on another vehicle