Good luck to you both. I had a stress fracture in lower shin from basketball a long time ago, and can tell you to definitely, decisively, stick with your doc's program.

Mine wasn't diagnosed correctly at first, and then the pre-recovery push of senior year and wanting to be a part of the team meant that I went back too soon and had a much longer recovery and much more pain (SO painful....worse than all my other injuries) than if I had gotten an immediate diagnosis and a plan for alternate exercise. I think there are other injuries where regular (non-sports) docs are too conservative, but stress fractures aren't one of them. So swim, do spinning intervals on the bike when you can get back on, but stay away from the running for now...