Except the bulk of deforestation is not caused by locals needing space to live, but by big entrepreneurs investing in wood trafficking, soy plantations and livestock production.
I don't think that was the point of the OP though. It was more that even with people trying to protect the forest through legal means of property ownership, there's an apathetic, and sometimes antagonistic government that won't enforce that, and will even go so far as to help those entrepreneurs against owners trying to protect the forest.
After setting up a space to live, the invasion kept cutting down more jungle to sell the wood and turn it into farmland. This is when they lost their support. I'm not a journalist, though. I saw the clearings and town myself. The rest is stories I heard by the fire.
If anybody really knows how much deforestation is of what kind, they are not sharing it very publicly. Much less the economic power of the people doing it, so one can claim they are "big entrepreneurs".
Anyway, that thing on the link you posted is not a forest, and really not the Amazon.