There must be more to the "science" than what is described here:
They begin with a puppet show. In this show, a gray cat is seen trying to open a big plastic box. The cat tries repeatedly, but he just can't open the lid all the way. A bunny in a green T-shirt comes along and helps open the box. Then the scenario is repeated, but this time a bunny in an orange T-shirt comes along and slams the box shut before running away. The green bunny is nice and helpful. The orange bunny is mean and unhelpful.
The baby is then presented with the two bunnies from the show. A staff member who doesn't know which bunny was mean and which bunny was nice will offer both bunnies at the same time to the baby. The baby's mother, who is usually present during the study, closes her eyes so as not to influence the baby in any way.
Which bunny do the babies choose? More than 80% of the babies in the study showed their preference for the good bunny, either by reaching for the good bunny or staring at it. And with 3-month-olds, that number goes higher, to 87%.
As described, the result is obviously equally compatible with the hypothesis that babies are born with an innate sense of self-interest. So what's the real story here? Additional links welcome. (Thanks to Mark Couch for the pointer.)