The K value is not a pure measure of soil erodibility as an intrinsic soil property.
The K values also includes some erosivity effects by how soil properties affect runoff, which is a significant part of what the variable K is representing.
The same storm occurring in August generally produces less runoff than the same storm occurring in April in a Midwestern location.
The other part of what the variable K represents is that K values are typically high in the spring as and immediately after the soil thaws.