The error in reasoning is to assume that the specific component values used in the example circuit have any general meaning.
I think, the example is discussing the special case where an amplifier is for some reason driven by a high impedance source and calculates the bandwitdh limitation caused by the source resistance. The schematic is misleading in so far as it doesn't show the resistance as part of the external source.
The calculation is also incorrect for all FETs with non-neglibible Cdg capacitance, where the bandwitdh is considerably influenced by the miller effect.