Can we rule out a scenario where disease was also implicated, like here in the Americas?

Incoming colonists were (and remained) genocidal by comportment, yes. But they also had the "advantage" of having a wave of smallpox and other disease going before them in a wave of devastation.

Farmers coming up from the Balkans and Pontic Steppe would have been living in larger settlements and among livestock for generations and would likely have brought with them things like smallpox that dispersed hunter gatherer societies would be less likely to encounter.