The study mostly focused on European cities because ... well, here in America not having parking is considered heretical.
I've written before about how when I lived in LA, I used to consistently drive places an easy walking distance from my apartment simply because I could. There was always ample parking. It was faster to drive and more convenient, so why walk to the sandwich shop a couple blocks away or the pizza place or the laundromat? Why walk to the grocery store, even if I am only picking up a couple things? I have a car and it has a huge parking lot.
On the other hand if parking had been scarce or expensive? You bet I would have walked.
Cheap and easy parking changes the calculus we make when we are deciding whether to drive or to walk or to take public transportation. For example, right now I take public transit to work every day. Public transit is almost as fast and it's relaxing. I'd much prefer to read a book on the subway than fight traffic.
Public transit is also cheaper. But it's ONLY cheaper when I factor in the cost of parking all day in a garage. Without that cost, even with the sky-high price of gas, it would probably be cheaper for me to drive. (Factoring in the cost of wear and tear on my car might change the calculation, but let's face it: most people don't factor wear and tear in when they're making these back-of-the-envelope calculations.)
When you make parking scarce and expensive, you start to then build your city for walkers and bikers and public transit. Without massive parking lots everywhere, your city may have more room for parks and gardens and playgrounds.
We don't have to make parking cheap and easy. No one really wants to pave paradise to put up a parking lot.
So let's not.