Natalie's slept on her tummy since we brought her home. She's more comfy that way, and it helps keep her hands from flailing. Swaddling made her MAD MAD MAD, so we eventually had to stop it or she wouldn't sleep at all.
Her ped gives us lots of dirty looks when she asks and we tell her, but too bad.
I did check on her a lot, but it also helped make her neck muscles really strong having to use them earlier, and she's been crawling a couple weeks now FWIW at 5 months.
A lot of reflux babies are more comfy sleeping on their bellies too.
Just another point of view.