Wow, I just have to say that the "Back to Sleep" campaign has sure been effective, if it can even make us nervous of stomach sleeping that the child initiates!!
ITA with your doc and the PPs...if the sleeping space is safe, and the child is healthy, there's no reason she shouldn't turn herself to her tummy for sleeping if it's more comfortable, and no reason (IMO) that you should insist she sleep on her back!
Our babies have all been tummy sleepers from the start--cosleeping on my chest or turned inward towards my side. And then when were big enough to roll to tummy, I even put them down for naps (in the crib, no toys/blankets/bumpers/pillows) on their tummies. They much prefer that position, and sleep much better, waking happy and rested.
Fret not mama!
Are you co-sleeping? If not, you might try it (or a co sleeper/side-carred crib) to give yourself some extra peace of mind!