K-factor does not tell you "all about stability" of a circuit but just a simple prediction.
As you know well, stability term is coming from classical circuit theory e.g.Poles, Zeros, Bode Diagram etc..
K Rolett stability factor has been developed in the same analogy and manner using with s-parameters and it's valid only and only for single stage circuits.This is important and shouldn't be ignored.
For a cascaded/paralleled/mixed topology circuits, it will not be valid anymore.