No, that's entirely sound. But trying to pick out (natural?) kinds based on words is a pretty silly idea from the start. It becomes even more painfully obvious when people realize that there is more than one language and `yours' and `theirs' don't always match up. And then trying to pick out (natural?) kinds based on conceptualisation in the first place fails as well, since there are multiple cultures, which may again have different views on the matter.
BUT, I would argue that picking out a range of ages based on two iterations of counting through all 10 of your fingers is a more natural and universal concept based on sounder and more natural terms than is the age range defined by the affix to numbers between 13 and 19 in English :P I guess the question is whether 13-19 has some other, more sound basis. For instance, some important biological function being mostly present in 13-year olds, but less so in 12, 11, 10-year olds. Not that language is based on useful functions though. I agree that, in many cases, it is not.
I guess all of this is (though interesting) totally tangential. In this case calling the 10 and 12 year old `teens' is more appropriate than calling them `pre-teens' because then all the more inapplicable associations with `pre-teen' (still unable to operate computers, etc. because they are 5yrs old) may have been misapplied. Had the child been 15, or 17, or 19 years old the story would not have changed much. But had they been 5, and been able to work out the cell phone usage and facebook etc., that would have been amazing in its own right. So, in the context of this story, they fit more into the `teen' category, than the `pre-teen' category. Though, I guess here `children' may have been sufficient.
Whatever :P