I don't have specific knowledge about carrying twins. And I've heard before what your doctor is telling you and understand his/her point of view. However, I will say that a mother's intuition is usually right. I would express your concerns to your doctor and see if there are other options. Maybe the babies can be monitored very closely after 38 weeks. There is something to be said for letting babies be born when they are ready, especially if you are doing so well.
As for those that say it's your body that decides when to go into labor, I would argue against that. If you want evidence to the contrary, I suggest you read books on the Bradley Method. Dr. Bradley has had extraordinary cases where babies went far beyond their due date to reach readiness and if they had been induced when those outside the womb decided it was time, they may not have survived. (Not to say that'll happen in your case, obviously, but just to illustrate a point.) Also, (it's been a few years since I've had a baby so I don't remember the exact mechanism that the doctor told me causes this) but changes in the baby actually trigger the hormones in the mother to give birth.
One last word, there are many twins in my family. My grandmother was one and she gave birth to twins and I have cousins that are twins as well. Not one set of twins in my family was induced and all were carried safely to term, so it's not unheard of to let the babies decide when they are ready.
I would just talk to your doctor. I've learned from my own mistakes NEVER to ignore your instincts as a mother.