If you'll read the information at the link above, you'll find that mention of the "House of David" is a matter of archaeological record. Such writing carries dynastic indices which, when coupled with other finds, shows conclusively that such an account as David & Goliath was well within the realm of possibility.
When we look at the facts we already know.....we can readily ascertain that such account or one of high similarity was not only possible, but probable as well, given the variety of battles settled by single combat.
We know what the sling can do, and to find record that someone actually did it is, to me.....no indication of embellishment.
TS