Thats understandable, but if you could ask if they know of any groups they could recommend that could possibly have a list that might help... and would keep from having them give you biased answers...
though of course ANY doula you choose would have to be someone YOU are comfortable with, not just someone you are stuck with... if its someone who is already comfortable with your doctor as well it would be a bonus in my eyes as they would already know ways of dealing with them better than a doula who works mostly with other doctors (as everyones different, even doctors...), including ways of helping to get them to allow you to be less restricted.
I really hope that all makes sense?