I agree that over-driving a speaker is the typical source of the distorted tone called "farting," but a speaker can accurately reproduce a distorted tone originating from one (or more) sources besides the speaker itself. These include the instrument electronics, onboard preamps, effects, main pre, and power amp.
Furthermore, I recall once when a speaker in my goliath II 410 stopped working and all the others started farting at low volume. I was pretty sure I had fried the drivers, but it was a loose speaker wire in the cabinet, and much easier to fix than diagnose.