Laurel isn't inside 24/7 but she absolutely does not use the back yard. We get in the car and go drive to a nice place for day hikes.
She is already 5 lbs and still a puppy, so obviously she needs more exercise than your two but a safe outdoor run is not an unreasonable request at all. We have hawks and wildlife here too--when the trail doesn't permit big doggies, our little doggies need to go into their slings or backpacks for their own safety.
I'll be asking my own landlord the same question next spring. If he says "No", I guess I'll need to get some sort of a playpen.
Laurel: born 9/1/18, 7 lbs, my homegrown
Chocolate: born 10/4/18, 9.5 lbs, rescued from DV situation