Barefoot-
Wow that's pretty scary. And a very compelling reason to not have the tests!
I had a similiar--albeit MUCH less serious--issue with my daughter. I was diagnosed with gestational diabetes and they wanted to induce labor at 36 weeks. I was NOT large and I kept the GD in check with diet. (Actually, I think I was mis-diagnosed.) If not for the midwives in my corner on this point, they MFM dept. probably would have pressured me into it. My husband and I got into it with one doctor, resulting in an apology phone call from the midwife and a note on my chart that this particular doctor was NOT to come near me -- ever. Fortunately, there were always two doctors on duty at the hospital should I have needed one, which I didn't.
My daughter was born 2 weeks late and only 6 lbs. 4 oz. So anyone can do the math on how little she would have weighed at 36 weeks... we would have been in NICU with a severely underweight baby.
Point: Trust your instincts on every matter. Doctors do NOT know everything and tests are not error-proof.
Sorry for threadjacking. And for being so anti-medical establishment.

Midwives and doulas on this forum, y'all rock in my opinion.