Obviously driveless cars would cause changes in behaviour, but I don't think it would be in the way the author suggests.
The idea that a large portion of people might give up car ownership because a car can drive itself doesn't hang together for me. As a consumer cars that can 'drive themselves' already exist, we call them taxi's. There are very few people though that prefer to rely on taxi's for regular use rather than own a car.
Which isn't to say that there aren't people who don't own cars, there are, and these people use public transport, taxis, feet, push bikes, etc, as they choose. But the kind of people that currently own cars will in the vast majority (IMO) continue to own cars, even if the car can drive itself.
Perhaps the author isn't a car owner, or maybe isn't a typical one. I'd suggest that a typical car has a lot of personal property left in it, all of which would need removing if other people had access to the car during the day.
There are a few points about groups of people who are unable to drive currently (children mainly), this isn't a group with a large disposable income, nor a high requirement for motorised transport that their parents aren't capable of providing. So driverless cars won't suddenly see 10 year olds taking self driven cars to the next town.
Anecdotal, but if I consider my own usage, today the car could have gone back home instead of me paying to park for the day, but generally I cycle and the car stays at home anyway.
There's nothing inherently impossible about my usage that would stop me using an on demand service that lacked ownership, but I don't use city club cars and I don't use taxi's for regular journeys, I expect that the same economic arguments would apply, owning the car would simply be cheaper and/or more convenient.