Disi....The chart represents a model, a proposed reconstruction. Debates are the lifeblood of science. Sure there are uncertainties about the minutia. Just as today there are those who argue for regarding Bonobos a subspecies rather than a separate species, there are legitimate debates about where to spit the species lines in the deep past. The best part of science is the process. New evidence is always refining the big picture.
That can be frustrating to those who impatiently crave absolutes. There is simply no way to be dogmatic (tho individuals often are) about the details. Sadly conspiracy theories (I include Creationism) thrive on uncertainties and complexity.
Ironically, the new DNA evidence has illuminated the pictured by making it more complicated. While there always those who suspected it, the DNA evidence from Neanderthals seems to support the intermixing of distinct line of hominids. Simple models that look like a tree are oversimplifications, (and are recognized as such) in reality there were branches that merged, more dead ends, and branches that occasionally bumped into each other while remaining largely separate. It looked more like a matrix, a network of lineages.
Fossils can only show changes to bone, DNA can show much more. Subtle changes in protein signals that effect changes in cognition and immunity. Unfortunately this wonderful new window into the past is very limited by time and environmental conditions. But the Neanderthal. DNA seems to be proof of concept, distant cousins can and did interact and effect evolution of our species.
My reason for posting the chart wasn't to assert that that exact proposal was the last word on the topic but to show the authors of the papers did not doubt the relationship of Neanderthals to us.