Sleeping on your back is entirely safe for the baby. But it is true that many doctors and midwives do not advise pregnant women to sleep on their backs after they have developed a significant baby bump. And besides that, most women find sleeping on their back to be extremely uncomfortable when they have a huge tummy. The problem with sleeping on your back after the second trimester of pregnancy, or earlier for some women (especially with a twin pregnancy!) is that the growing uterus will put pressure on the vein that returns blood from the legs to the heart. If you lie on your back long enough, that can interfere with your blood flow and cause blood pressure changes.
Personally, I don't think that you'd keep that up long enough for this to start causing problems for the blood supply to the placenta, and therefore your baby, because you would feel uncomfortable and simply change position. Most pregnant women sleep on their sides or curled up, and many like having a full body maternity pillow to help them find comfortable sleeping positions. Indeed, sleeping on your back is not the best position, but if you feel like napping on your back sometimes and feel comfortable that way, you will be just fine.