As @cosmopinkice points out the research and information seems to be a bit vague both on what is too young and what is too far when it comes to having kids run distances. However, the American Academy of Pediatrics issued a policy statement outlining the risks of distance running in children. The statement is a bit vague, but addresses the risks for children (many are the same as for adults) and also outlines a couple of unique elements – (1) Children are growing and so there are some unique risks to growth if they do too much running and (2) children may not be as sensitive to the feedback that their bodies are giving them which can create greater risks.
All that said, the far bigger problem in children today is obesity, so getting your kid off the couch and outside running is a great thing. If your kids enjoy running, let them do it, but keep their distances in check. Most kids’ races are half a mile to two miles, which is probably appropriate for that age. Let them progress to longer races once they get into their teens.

I tried to research a really good answer for you. I didn't find a great deal of information on this subject. I have a six year old boy, so of course this was interesting to me. I did run across a few good articles, but these don't necessarily state ages and stats, but just more or less say "young children".

http://www.halhigdon.com/kidsrunning/index.htm

In the above link, a Dr. Metzl is said to believe that the positives of running outweigh the negatives. We live in a world were children are being check indoors playing video games, watching t.v. and eating junk food. Childhood obesity is soaring, and teaching children at an early age to be active is good. The article also suggest that by getting your children involve in something like running, they are less likely to turn to drugs, cigarettes, etc...

The other article, http://www.oztrack.com/devsp.html, says that it is very important to teach children to run correctly and proper training to build up. More of a jog or sprint, with proper posture.

I think running in moderation is great. It's extremist that might be causing more damage than good. I think any parent should discuss this level of activity with their pediatrician.