Your doc says it's OK because a rib injury is one of the easiest to run with, for many reasons:
(1) You have nothing to gain by sitting around. Whatever tiny amount of pain you save now, you will pay for in lost fitness later.
(2) Any other exercise or cross training is likely to involve the ribs as much or more, and be just as painful.
(3) Keeping yourself moving will help to increase healing circulation and "model" the repair of your ribs and surrounding tissue, so you are less likely to experience secondary issues later.
(4) You are going to sneeze and cough anyway, no matter what you do.
(5) It will help increase your pain threshold, one of the most important mental roadblocks on your way to being a successful competitive runner.
There are more reasons, even some for not running, but they are far outweighed by these advantages. One caution I would emphasize is to avoid any kind of running that increases your risk of aggravating your injury with bad footing or another slip and fall, at least until you have a month or so of healing under your belt.
Thanks for the advice. I spent the week getting to know the exercise equipment at my gym (hello stationary bike!). Later in the week, I did a couple days of short treadmill runs, and my ribs felt okay. Sore and stiff but not too painful. Today (one week later), I ran 10 slow miles outside on pavement. So far so good. We'll see if I am sore tomorrow. The pain meds I am on are pretty good at taking care of the pain. Also, I went to the doc yesterday for a follow-up x-ray. Bones are definitely broken, but my lungs are good. Doc says running is okay. I just need to make sure not to suffer another blow to the ribs. They are weak now and even something minor could be very serious. Treadmill should be safer than running outside. Definitely no trails for a while.