Well, the law is new, just not as new as the article says. And I'm just not sure about the trail access. It just isn't clear. I suggest either checking signs, or local park authorities. Either that, or just use the trails until someone says otherwise. You can trot out the law and at least give the impression that you've made a good faith effort to be law abiding.
I 've walked many trails in McDowell Mountain Park doing bird photography (http://www.jayandwanda.com/birds/birds.html). But I've never really biked through there. The one time I did it was on my road bike and I used the paved roads not the trails. I then hiked to the park's perimeter and climbed a barbed wire fence. I was looking to see if I could find a good path to Dynamite road and avoid having to ride through Rio Verde.
Anyway, McDowell Mountain Park has lots of nice multi-use trails. And I don't recall ever seeing anything like park ranger patrolling. So as long as you don't ride like a maniac, you should be OK. Beyond that, I just don't know. I'm mostly a road rider and use my ebike to commute from Fountain Hills to Scottsdale Airpark area.
