Which means exposure is the wrong tool — that's flooding, and it makes fear worse. Decompress first, find the distance where they can still eat, then change how they feel about it.
Puppies are socialised by positive exposure. An adult dog that's already frightened just rehearses the fear at close range — which is why the park trip that was supposed to help set you back a fortnight.
Behaviour in the first fortnight tells you very little, and some of what looks like deep-seated fear softens on its own once the dog settles. Almost no plan starts here, and it's the step that makes the rest work.
A dog that won't take chicken it would normally mug you for is over threshold, and nothing useful is being learned at that distance. More distance — not more encouragement, and not a better treat.
Well-meant, and one of the commonest ways owners lose ground. A frightened dog approached by a person holding food is being asked to choose between two things it's afraid of.