I strained a tendon 7 weeks before my first HM. The doctor didn't say not to run - he just gave me that one-eyebrow-raised side look that pretty much say "doubtful." He said I probably wouldn't make things worse, but that I would hinder healing. I stay off of it and did the ellipitcal and some swimming instead. It didn't hurt on race day, but it swelled up a bit. All in all it took about 8 months until both the pain and swelling was gone.
That was a strained tendon. Surgeries are another story. When you run your body pressure increases. If you have recently had surgery, you're placing pressure on an area that is already compromised, so in very layman's terms, you can easily "blow it out." Not a good thing.
If I'm sick with cold or flu I will run according to how I feel. If I'm coughing, fever, etc. you better believe I'm not even looking for my running shoes. I'm looking for the chicken soup pot.
"God gave you your body as a gift, so you should take care of it." - My Mom