I propose the following errata:The White Hand: Wild Horses
Resource: Faction
Playable at any tapped or untapped non-Haven site in Rohan, Southern Rhovanion, Khand, Dorwinion, Horse Plains, or Harondor if the influence check is greater than 11. Standard Modifications: Men with home sites in the regions listed above (+3). Tap this faction to allow any company with one of these regions listed above in its site path to move up to 1 additional region.
"Playable at any tapped or untapped non-Haven site in Rohan, Southern Rhovanion, Khand, Dorwinion, Horse Plains, or Harondor if the influence check is greater than 11. Standard Modifications: Men with home sites in the regions listed above (+3). If a company's site path that use region movement would contain at least one of these regions listed above, you may tap this faction to allow the company to move up to 1 additional region."
Rationale:
Original text of the card is the example of ICE's twisted tales, where conditions are mixed with results.
Until all effects that allow a company to use an additional region (card) will be applied, it is not known whether its site path will contain some region, or not (beside a region containing a site of origin; but even it is hypothetically subject to change).
The modified text checks whether final company's site path would contain at least one of the listed regions and only if the result of the check is positive it allows to tap the faction card for effect.