Cross-listing a ruling here from the Duke page:
If you have Frozen in Fear in your threat area, using Duke’s first ability [Fight] would require spending an additional action, as it is a bold action matching Frozen in Fear's restriction. Using Duke's second ability is an action that does not match Frozen in Fear's restriction, so it does not require spending an additional action.
This squares with the rulings above, that the bold action designator is the critical part, and not the fact that you end up in a different location. So Duke is as much an emotional support dog as a bloodhound.