Yes, new parents are strongly advised not to put anything in a baby's crib other than the bottom crib sheet. The good news is that the rate of "sudden infant death syndrome" has declined dramatically!
The first decline occurred when parents were advised to put their babies to sleep on their backs. The second came from eliminating every non-essential item from the crib. Hard to argue with these results, especially if you've lost a baby to SIDS!
I agree with Quilt1950's commitment to making "floor quilts" for babies. I assume that s/he uses some sort of flat batting, as anything puffy would put an infant at risk.
I've only made one baby quilt so far with this in mind, but the parents were ecstatic! The quilt came with the promise of washability and the plea that it be used rather than cherished - a winning combination!
Sushi