Increasing the distance between charged plates in a capacitor will always decrease the electric field strength and the capacitance proportionally, regardless of the materials used between the plates.

The statement is false. The electric field between the plates is the voltage divided by the distance, so for a fixed voltage the field decreases as the plates move apart, but the capacitance depends on the permittivity of the material between the plates, not just the distance. Capacitance is given by C = εA/d, where ε is the permittivity of the dielectric; changing the dielectric changes ε and therefore C, even if the distance stays the same. For example, if you insert a plastic sheet with a high dielectric constant, the capacitance increases even though the distance is unchanged. Thus the effect of distance and material are separate and not always proportional.