FWIW, when I've had knee and foot flareups, I've found an elliptical machine is an effective way to "run" without any impact. It's helped me. (Alas, I don't have access to one right now, but fortunately don't have any flareups.)
My sense on walking is that it helps for general fitness, but not for referee fitness. We need to sprint (among other things), which is a different demand on our cardio and leg muscles. (Aside: when I was in high school, one of the guys on my basketball team was a water polo player--a very good one who I believe went on to play in the Olympics. And, well, water polo players are in amazing shape--I remember walking by their practices where they were treading water while holding folding chairs over their heads. But when he got to basketball practice, which started right after water polo ended, he would die on the basketball court because it was so different.)