Engineering school or no, they were very much engineers in the modern sense of the word, and careful theoreticians as well. Though they did not invent the wind-tunnel, they put it to much better use than any of their competitors. Their greatness lay in their ability to separate the various parts of the problem of powered flight, and solve them separately. lift is a separate problem from drive, and both are separate from control. Their careful (and extremely courageous) glider tests revealed the necessity of three axis control. Yaw and pitch were already understood; roll was not. By separating the problems of lift, drive, and control they were able to concentrate themselves on the parts of the problem they understood best (lift and control) while hiring out the problem of drive (build a powerful and light weight motor) to a friend who understood that issue.
To call them "bumpkins" is to greatly misunderestimate them...
Don't kid yourself. The Wrights did benefit from Langley's work. For one thing, they learned what didn't work. As you can see from the description, the Langley machine was a decent glider, it glided almost as far as the Wright machine flew under power on that first flight. The Wrights were engineers, despite not having gone to engineering school. (Not all that uncommon in that day) If they couldn't figure something out from first principals, as a physicist would be wont to do, they experimented until they found what would work. The built wind tunnels to determine the best shape for their wings. They flew large "kites" to learn still more about what would work.
They also knew that weight was as important as power in the selection of their engine. They chose a very low speed prop, which could get by with a very light drive mechanism. But saying they did it "all on their own" is to misstate the history of the effort. They, like all pioneers in such areas, benefited from the previous work of others, and also from work in unrelated fields, gasoline engines, driven by automotive needs, in this case.
That is of course not to say they don't deserve lots of credit for perseverance and ingenuity, they do, boy do they.