This is a fascinating article but I think it is important to note this is based on evidence from the BOLIVIAN portion of the overall Amazonian rainforest, which is and was on the periphery of the rainforest proper, and still at its most extreme North-east point almost 500 miles from the Amazon river.
No telling that the forest itself was smaller or not there at all, but my (uneducated ) guess would be there were still vast regions still under forest while Bolivia was savannah. The whole rainforest area now is almost the size of the US East of the Mississippi.
I wouldn’t extrapolate an overall theory about the rainforest from evidence in Bolivia alone.
A most excellent BBC documentary on the ‘dark earth’ (Terra Preta) of the Amazon. https://www.youtube.com/watch?v=-YS8I6AZRfg
A paradigm shift is going on in regards to the Amazon Rainforest; no longer can we go into any part of the forest and assume it is pristine. Millions of people (est. 5-6 million) once inhabited the region right up until the arrival of the Europeans. There is evidence many of these lived along the Amazon River.
So far an area twice the size of Spain (in the south) is now known to be anthropogenic - this is growing all the time with new archaeological discoveries.
To my mind it makes little sense that parts of the Amazon are only 2,000 yrs old while remainder is 55 million years old.
It may swing back and forth as these things have a habit of doing but ultimately I see future studies confirming my stance.