Maybe. Though a bit of a different take, a lot of tribal communities care a lot about legacy (theirs, that of their forefathers, etc). That legacy is really what defines a tribe, and if a tribe loses its legacy, it risks falling apart. And if it falls apart, then it is vulnerable to predators eating its herds, tribes stealing members of its family, inability to find food / water. Legacy is more collective than fame (at least the modern, Western version of it), which is a lot more individualistic.
It's not so much fame as legacy. The fear of a legacy (or your ancestors or your lineage) being forgotten is very, very real.
(I am from the Middle East. Obviously centuries later here, but I still feel like legacy is a big cultural factor for most Arabs)