J.M.
When I had my first daughter I was diagnosed with a low lying placenta. I thought I was doomed, I wanted a natural birth only. My doctor's office never gave me measurements (this office tends to not give out that sort of information to patients so the patients don't needlessly worry). SO I can't tell you exact measurements, they did however assure me that if there was an issue that there would be an operating room etc. in the rare event that I needed it. They told me that many woman have natural births all the time with this condition... which I am happy to report I did. However, I did bleed a lot for an extended period of time after my daughter was born, to the point where they wouldn't move me from the delivery room to the post delivery room. After about 2 hours it slowed enough on it's own. They were never overly concerned, it wasn't a major issue, just something that is common and should be watched.
My advice to you is if you don't like what your doctor is telling you, quickly go and get a consult with another doctor. I know it would be a pain to switch now, but you can always get all your records switched over, and you may like a new doctor better. I don't think it's fair when the doctor isn't willing to consider any other options.
Otherwise have a heart to heart with your doctor see if you can persuade him to let you try a natural birth. I don't know how sympathetic he will be to you being that he will never understand exactly how you feel, because he can never experience pregnancy, but only you know that. Good luck, and don't be afraid to ask for what you want!