Is it possible to get Flux in a magnetic circuit with zero mmf?
In the example, the core permeability is assumed infinite (it says it in two places). With infinite permeability comes infinite inductance and therefore any reasonable AC excitation (frequency greater than zero Hz) will not cause any current to flow hence ampere turns or MMF and H (ampere turns per metre) have to be zero.

Further down they discuss two real materials that clearly don't have infinite permeability.