Interesting question, and I agree that the iaaf documet is an interesting read. However, table 4.6 strikes me as potentially being a bit over-cautious......
My son is 7, and he has just started doing Parkrun with me, and as Caroline says there are plenty of other kids there who are probably under 9, who according to the table should be running a maximum of 3km a week.
Obviously, I know that my son isn't "competing" over 5km, and I try and make the parkrun a fun activiity that we do together, but there are times when he is very determined to beat his previous time, or to catch up with the little boy who's ahead of us, etc..
Chris - Personally, I think some runs of 2-3 miles is a good start, I would definitely recommend a Parkrun, and I wouldn't be too concerned about a 13 year old building up to running a 10k