This is a myth. There is no reason that channel spacing need limit the modulation bandwidth. The only downside is that listeners to adjacent stations will hear a slight "monkey chatter" from the overlapping sidebands. In reality stations are never allocated adjacent frequencies within the same coverage area so this usually doesn't happen.
Be that as it may, AM radio is obviously low-pass filtered. It might not be a brick wall at 5 kHz, but it sounds obviously muffled to someone who can't hear anywhere near up to 20 kHz. If I were to guess, based on years of experience of playing with EQs, I would say that it has next to no content beyond somewhere around 8 kHz.
AM receivers have to apply a band pass filter to select the station. The width of that filter will directly affect the audio bandwidth. The filter probably can't be anywhere near +/- 20 kHz based on the idea that nobody nowhere would put two stations close together in the same area. Mass produced AM radios have to work everywhere.
