I don't know if it is faithful to the book, but everything in Greystoke makes you hate White Anglo Saxon Protestant culture and love hairy monkeys, which is absurd.
Given that the original novels and older Tarzan films are seen as racist towards non-whites, this makes up for it. Burroughs would have us believe that just because Tarzan was born to English aristocrats, he would be superior to all jungle animals and natives.
An upper class white man will excel at even savagery if that's the only path offered him. This film takes on modern sensibilities that civilization is not the opposite of savagery but rather hypocritical. Tarzan lived in a kill or be killed world, to see that civilization kills for sport or gain made him hate it. If you find our world perfect and are uneasy with questioning it, you may want to stop seeing films or reading novels as this theme comes up a lot. It doesn't mean we should hate ourselves, just think about the world around you.
As an English white Anglo-Saxon Protestant and proud of it, I thought the movie was pretty well-balanced. It showed that the Victorians were responsible for a quantum-leap in human understanding (they gave us Darwin, after all), but that that understanding came and continues to come at a terrible price in cruelty, destruction and arrogance.
If any group got short shrift it was the ruling elite and landed gentry. And it served them right, in my opinion. But then; I'm just a commoner.