As a parent you must make your own decisions as to what "recommendations" you will follow. I have a 3 and 6 yr old and I (gasp at the horror) allowed them to sleep on their tummies as babies. One had acid reflux and the pressure on her belly made her feel better....so she slept....and so did mommy!
However my son is 3 and he has a big boy bed (complete w/ a quilt i made him) and just the other day we found him w/ his sheet wrapped around his neck 3 times and it was TIGHT! he's fine but now has no sheet on his bed! just his blankies & quilt. It's all relative to what you feel comfortable with and the things you've seen and lived through in your life. never did I think a sheet for a 3 yr old (heck they make sheets for toddler beds!!!) would be something to worry about. But my 6 yr old sleeps w/ a sheet just fine. I think the 3 yr old just rolls around a lot so something thin like a sheet isn't good for him. just go w/ what you feel comfortable with.