The Amazon deforestation problem is not the chopping down of a few trees, but large scale clear felling of large tracts of land. Think two bull dozers with a chain inbetween driving forwarding, clearing everything it's path.
Another problem, but smaller is single plots of land cleared to make way for a family to farm / raise cattle.
They don't care who owns the land.
http://www4.ncsu.edu/~rjdoming/