I actually have taught skiing and snowboarding (and tele) for over 20 years. And have heard this type of story quite a bit. I always tell parents it just depends on the strength of the individual child what and when they start. As we all know snowboarding is a bit trickier to balance when you learn, the skiing stance is a bit more natural.
On the other hand statistically snowboarders are injured far more often in the first few days ( I think something like 87% of all reported snowboard injuries happen in the first two days someone boards) where the opposite is true with skiers. As skiers improve and ski faster their injury rate rises.
The end result is I think kids should do both if they can, but if they are going to start to board, get 'em on early where while they are younger they are less likely to get hurt due to their flexibility and the fact they don't fall quite as far as us 39 year old boarders do....I have lots of kids in my classes that do both and just choose by what the conditions are like what they want to do...
Allot fo these stats are available on the National Ski areas association website (www.nsaa.org