The back pain due to injury is true, but the reason he sat down that way isn’t because of that. Frakes confirmed in an interview that he did it because he thought that would showcase Riker’s cockiness. Nobody stopped him from doing it, so it stuck.

The back injury, however, is the reason behind the “Riker Lean”.

His maneuver is only impressive when you realize he does it for the challenge of not hitting the chair over with his massive genitalia.

For the curious, it was actually chronic back pain or something like that. That was the least painful way to sit

See, I feel heard in this. Not to brag, but I'm 6'4" and "things" are proportional. I sometimes step over stuff that others wouldn't, but I'd hesitate at a chair. There's too much risk, he'd have to have a tight nutsack all the time.