The panels usually show you the "local" transform, or rather, the transform relative to the parent, which is an object's world transform multiplied by the inverse of the parent's, with the angle being derived from the world orientation based on rotation order, with the spins counted (as a singular 4x4 matrix can't account for spins, only for an orientation, when it comes to rotations).
That page might seem confusing because it's telling you what Maya considers to obtain the final transform, which is a long chain of operations on different components to make sure that all things that can affect a transform in maya (such as the pivot) are accounted for.
The inversions should be addressing the pivot's behaviour, and without trying, I'd guess it's implied as invert the result of the chain at that point, so first invert the scaling pivot, keep going, then in the chain of operations once you've factored in the rotation pivot invert again and keep moving.
Again, without trying and at a guess, without those inversions I'd imagine you would get a double offset from the pivot if it was non-ID instead of it affecting components the way you want it.
Have you tried implementing your own reconstruction of it to see it happen at the various stages? It should all become fairly clear compared to trying to figure out the hundreds of operations in your head
Most things like missing an inversion should have a visually meaningful repercussion, and show you why it's there (IE: Pivot compensation becomes mirrored or additive instead, matrix changes handedness and stuff like that)