It is partly true.

All babies have a reflex that makes them stop breathing for a short while. This reflex is triggered when the face is put underwater, as well as when you blow a gust of air in his or her face. You yourself can feel the remainders of this reflex if you try to breathe with a strong wind in your face.

This does not mean that babies can swim.

Triggering this reflex is not very comfortable for the babies, because they can't breathe for one or two seconds even when they are out of the water again.

Source: We just finished a baby swimming course, where the toddlers are accustomed to the water and to being underwater without triggering this reflex and without drowning. I can highly recommend such a course.

Good question, I was wondering that, too.

When I looked this up I found an interesting piece of advice / warning from babycenter.com: "Don't put a baby less than 6 months old under the water. Although infants naturally hold their breath under water, they continue to swallow."

We wanted to get our daughter into the water early to preserve her water instinct.

We started her on swimming lessons at 3 months old. Whenever we put her under the water it was only a brief dunking (about as long as her reflex lasts - say around half a second). She got used to it fairly quickly and only complained when she got tired of it (after 6 or 7 dunks over a half hour).

We won't think of putting her underwater for longer than that until she can hold her breath on command.

I've never heard about the supposed ability to swim, though. That seems rather ridiculous, given their lack of strength and motor control.