Spot on, anybody's name can be on the logbook doesn't mean they are the legal owner.
And no if your name is on the log book you don't have to be insured to drive it. I had a 1990 MG Metro Turbo (I know it was my first car when I was 17, hoping it would become a classic, its was never gonna be) rotting in a garage in Wales for a few years. My name was on the logbook but I wasn't insured to drive it.