The subtlety here is the difference between a perfect conductor and a superconductor. These are not the same thing!
For a perfect conductor, you expect the material to perfectly resist changes of the internal magnetic field. Thus, you expect that if you start to apply a field , the field will be perfectly screened.
But consider a superconductor in which you apply a magnetic field above the critical temperature T_c, and then cool below T_c. If it were just becoming a perfect conductor at T_c, then it should only care about the rate of change of the magnetic field, and thus it would be perfectly content with the internal applied field.
However, in reality the superconductor expels the magnetic field in this situation (the Meissner effect). This is related to the fact that the superconducting state is a thermodynamic, collective phase.
So the difference between a perfect conductor and a superconductor (for the purposes of this conversation) is that the former perfectly resists changes of the internal magnetic field, while the latter perfectly resists any internal magnetic field at all, whether it is changing or static.