The prehistoric Indian of America ususally buried their dead in the flex position (on their sides). So when you say old practice, that is not an understatement. lol
Burials in the north (modern Alaska, and adjacent areas) have been excavated, in which the dead were tied up into a fetal position, then buried. Not sure where else that was done, as precolumbian human remains in lower North America are rare. Some tribes used excarnation (consumption of remains by animals, typically birds; a similar practice is found even today among Zoroastrians -- just to clarify, this doesn't mean that the Zoroastrians are from precolumbian America, nor does it mean that Precolumbian Americans are from Zoroastrians), some used burial, some built elaborate tombs, even pyramids.
Regarding these three Iranians, I'm thinking that they may have been from Anatolia or the Aegean, as jar burials in the fetal position were common at one time (and were not a Greek practice).