My understanding of that is that all reptiles have a basal ganglia, because it was inherited from the common ancestor of reptiles.
And non-reptiles don't have a basal ganglia because their ancestors didn't have one.
Mammals and reptiles share a common ancestor with an ancient amniote, not a reptile
> Synapsids[a] are one of the two major clades of vertebrate animals that evolved from basal amniotes, the other being the sauropsids, which include reptiles (turtles, crocodilians and lepidosaurs) and birds.
> the only extant group that survived into the Cenozoic are the mammals.
> The animals (basal amniotes) from which non-mammalian synapsids evolved were traditionally called "reptiles".
> It is now known that all extant animals traditionally called "reptiles" are more closely related to each other than to synapsids, so the word "reptile" has been re-defined to mean only members of Sauropsida (bird-line Amniota) or even just an under-clade thereof
And do living reptiles, today, not also "have a basal ganglia which evolved from reptiles?" seems we've a name collision, here. Perhaps we should refer to our ancestors as "proto-reptiles," or else our contemporaneous cousins as "post-reptiles" whose brains have had just as many years' time to depart from our common reptilique ancestor.