“That doesn’t make any sense since there have been (and currently are) many great tzadikim among the chasidim that remained chasidic and many that were not chasidic but became chasidic. “
You’re right. I was putting out a counter-point to show the silliness of the OP. Speaking of which, all Chassidish rebbes can credit their non-Chassidish ancestors.
Seriously, AFAIK there was a lot of cross pollination between families and ideas, so everyone has some of this and that. Furthermore, it’s not for us to judge Gedolim.