Official comment
How were the coordinates for your GCPs measured? What are you comparing it to?
The adjustment we do is primarily in X and Y so assuming your have good input coordinates the outputs will be pretty darn close. The heights will depend on the accuracy of the initial processing and the accuracy of your GCPs. The initial model is tipped and tilted and raised or lowered to minimize the error between the points you define. It looks like there is some tilt in the remapped version from SW to NE.
Choosing GCP locations that are further out towards the edges will minimize the measurement error that gets introduced.
It looks like all the elevation values are pretty close on your GCPs.