I updated all of my schematic symbols and saw that the pin swap properties from your screenshot were visible. I used the xDx "PCB Interface" and PADS "xDx Designer Link" tools to attempt a push and pull of the changes to the PCB. No improvement that I can see.
I reverted to my schematic symbol and removed the pin swap settings in PADS Part definition (set all terminals to swap=0). That also did not solve the issue.
Regarding the pin swap, it would have been nice that the paired pins were swappable and that the pairs themselves were swappable. That is logically correct for the component to be mounted. The swapping of terminal pairs is exactly equal to rotating the part 180° so although PADS does not seem to support that kind of swapping it's value is pretty minimal. For this particular project it turns out the swap settings overall are a "don't care".
As a sanity check I have used the cross probing feature to show that when I highlight parts in PADS they are highlighted/focused in xDx Designer. The converse is also true.