You'd be fine. Leigh's point is trying to not exhaust you while you're on a big deficit. Plus, I'd always stick with what one likes and will do AND IS WORKING over something that someone stuck in a plan for the masses, even if it's as good a plan as OPT.

You'll be fine with your nice walk, it'll get you a good amount of movement, and then if you stop seeing results you have something you know you can try changing to conform more to the program and see if that works.
For me, the cardio there was a bit too much, and I'm fine on what I'd equate to your hilly walks with your dog.
(Plus, you can use machines if you want, she's giving a routine that could actually be done at home with just a bit of equipment, and so just lists the freeness of going outside over the costliness of having a treadmill/elliptical/bike/what ever.)