I always put the boys in something that has feet in it, otherwise, they get cold. However, I have always permitted my children to sleep with a blanket. I had read that it was okay to do so, as long as it was a light blanket and tucked in. My oldest really, still doesn't like to be covered and even if I put him in the flannel pj's with feet, he will unzip it in the middle of the night, get undressed, then climb back in bed with no blanket. My other 2 though, they don't like to go to sleep without something soft and warm touching them. The one always sucks his thumb and pulls the blanket so it's touching his face, but not over it. The other one, just likes to make sure it is where he can hold it. Both always have the blanket tucked underneath them and under their arms. also, because they move such, the one likes to hide under the blanket at times and then laughs hysterically thinking it is funny, that he is covered. However, we always check on them several times and especially one last time before we go to bed, to make sure they have not accidently covered their faces. The blankets are afghans so many holes, but very warm too.
Also, once a child moves around, it is difficult to keep them on their backs or even their stomachs, they will always go to a position they find comfortable to sleep.
Do what works for you and your family. If they truly knew what causes sids, it would not be called sids, it would have a name that describes the actual problem.
Good luck