Let's just think about capitals. London? Brussels? Paris? Berlin? Dublin? Lisbon? Bern? Rome?
None of these places are car free. You can go on Google maps and see cars everywhere. So we know 'all' is nonsense for a start. And 'most' is looking pretty doubtful already.
It's possible that the GP is comparing against their experience in American cities. If that is the case, then yes, most European cities are "car free". I would qualify Amsterdam, for example, as "car free" even though it technically isn't, it's just not a city I would ever think of driving in because every other way of moving around, including walking is so much nicer and you see few cars compared to any place in the US. Many times when going to towns in the US I notice than myself and my wife are the only people walking on the sidewalks for considerable amounts of time.
I don't know how someone can say something so obviously and demonstrably false with a straight face.