Until you have one drown, I'm sure you don't believe it.
The Storey Guide to raising ducks advises that you put pebbles in the bottom of a chick type waterer for the first few days. I haven't found that to be necessary,but you never know . . . .
I've never had a problem with chick type waterers. If they are a day or so old, they could drown in deeper water. Wait until they are older until you give them deeper water.