The below-the-line text in the client ("If Duchess is in the Supply...") does not match the below-the-line text in the newly released updated rules for Hinterlands, which still says "In games using this...".
The wordings we have that Stef got from Donald's forum (he double checked yesterday and it wasn't changed) say this:
Duchess: Action, $2
+$2
Each player (including you) looks at the top card of their deck and may discard it.
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If Duchess is in the Supply, you may gain one when you gain a Duchy.
So my guess is that the document you're referring to either isn't from the 2nd edition Hinterlands or they missed the change.
wero has it right. We got worried that the new wording of Duchess wouldn't be clear enough, and the wording in the rulebook on RGG's site is the actual wording on new printed Duchesses.
From the physical card:
Duchess: Action, $2
+$2
Each player (including you) looks at the top card of their deck and may discard it.
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In games using this, when you gain a Duchy, you may gain a Duchess.
That post of wordings on my forum, that was for people to argue about what the wordings should be; it will not necessarily have any late changes.