Its taking me a bit to get my head around where we disagree Steve, so I'm going to start from the basics and you can tell me where I'm going wrong. I don't claim to be an expert, and if somebody can show me how I'm wrong then I'll believe them, but your explanation isn't really doing it for me. And yes, you're right, I should have said COG, lets skip IC for now though.
Brake squat is the tendency of the suspension to sink in under braking.
Brake squat can occur at the same time as the shock extends. Heres where my explanations get tricky and hard to understand I think: The bike will "squat down" even as the shaft extends, because the shaft is extending due to shift in riders weight (forward). There are two parts to the mix here (and I'm going to assume you're not pedaling, because I have no idea how to explain what happens at that point). There is the brake/wheel/contactpatch whatever pushing the swingarm to compress the shock, and there is the forward shift in riders weight as they slow down (which unweights the shock, causing the spring to want to decompress and extend).
I think we still agree at this point?
If the sag point compresses, the the riders shift in weight is less then the brake induced squat.
If the sag point decompresses, the riders shift in weight is more then the brake induced squat.
The reason the bikes rear wheel stops working so well is because its suddenly oversprung when you apply the brakes. Squat attempts to keep the bike steady in its travel and keep it balanced without excessive pitch forward, but supposing your weight is 70-30 or 60-40 rear wheel-front wheel, when you brake it suddenly changes to 50-50 or 40-60 R/F. You have less weight over the rear wheel, and so whatever spring (or air pressure, whatever) you were running that was the correct springrate for you at a regular sag point and regular balance is suddenly too stiff. The suspension cannot react to bumps as efficiently.
Hypothetically, your springrate should change throughout the normal movements of the bike. For regular riding, it should be (hypothetically) a 400 lb spring. Then, under braking, it should be a 350 or 375 lb spring. Then, as you stop braking and start pedaling, You should be back to a 400 or 425 pound spring.