Got the answer from BMD Developer Support (fairly quickly too!). It’s a half duplex card. Full response below for reference:
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The DeckLink HD Extreme 3D is a half duplex device, so you can capture or render, but not at the same time. Therefore the E_ACCESSDENIED error that occurred is expected behaviour. The InputLoopThrough sample is intended for use with two DeckLink devices.
To perform the capture – modify – output process that you mentioned, you will require another DeckLink device, or a single DeckLink Duo or Quad card
( https://www.blackmagic-design.com/products/decklinkquad/models/ ). The Duo and Quad cards are basically multiple DeckLink SDI devices on a single card.