Gandalf calls Aragorn the world's best hunter, and Aragorn literally listens to the earth (in the pursuit of Merry and Pippin) like the Ranger class skill. If D&D isn't based on LOTR, weird that so many of the classes are 1:1.
Then look at the way Dragons in D&D affect their environment (e.g. the weather changes as you get near a dragon's den) and it's even more obvious that D&D is based off LOTR. Not to mention the assault on Minas Tirith beginning with a change in weather due to the power of Sauron (or the way Saruman changes the weather on Caradhras). Or look at the mechanics of being frightened, that's pretty much the core class trait of the Nazgul.
Reading LOTR after reading through the Player's Manual makes it extremely obvious where each of the class skills came from - the came from events in LOTR.