Lily was a tummy sleeper when she was tiny. She was always on a flat surface and never had any blankets around her face or anything. We coslept until she was 5 months old. By then she was rolling around all over the place and pretty much slept however she ended up.
I never had any worries about it. I was actually more concerned about positional plagiocephaly if she had been on her back all the time. When we were babies, doctors told our moms not to put us on our backs to sleep because of the choking risk if we spit up. I think that every generation is going to have different ideas about what's right and what's wrong.
I say do whatever works for you.