Child bathtub accidents

NY Times says:

Writing this month in the journal Clinical Pediatrics, researchers from the Columbus Children's Hospital in Ohio said that when they looked at bathtub injuries over three years, falls caused by slipping were the most common. And four out of five times, an adult was present.

I wonder if anyone has looked at the possibility that a mom's supervision actually increases bathtub accidents. The child may have a false sense of security by having his mom nearby, and not be sufficiently motivated to take safety precautions.