Steve,
Back to the original question for a moment...
I am indeed confused.
I can see why the lower springs could influence the desired settings, such as the toe or perhaps the camber, but why would the wheels/tires themselves be a factor at all?

As I will now state for the third time, wheels and/or tires DO NOT affect the numbers on the machine. If it was at 3mm toe with one tire it will be the same with another.

The point is that changing tires changes the loading during driving. The specs that are given are a compromise designed to apply settings in a motionless state that will place things correct when driven. that is why the toe spec will have one set the front toed in. As the car drives down the road the rearward force deflects all the suspension pieces rearward. This makes the car pull itself relatively straight even though it were set toed in. Placing larger more agressive tread changes the relationship between motionless and loaded. This requires new specs. They aren't in a book they are the result of experience and observation. Its the reason all these huge tires wind up with inside tire wear. They were set to specs but in actual driving the real alignment winds up toed out under the heavier load.

Thanks Steve.
I actually get it!
That clarification was very helpful.

yes, thanks a bunch steve! This is all making sense now...