I don't think that's true. I would certainly classified the tribes in the Amazon who get killed or pushed out of their homes by loggers and ranchers as displaced due to deforestation.
If you are imagining a rain forest as something full of people, just forget it. For population density concerns, the main difference between a forest and a desert is that people can traverse the desert, so you will find way more of them there.
When tribes and agriculture exist near each other, you will see economical interdependency, not one population pushing the other away.
