Competence in one domain translating into a subjective perception of competence in an unrelated domain
Solution 1:
The "halo effect" is defined by oxforddictionaries.com as
The tendency for an impression created in one area to influence opinion in another area
Usually, this term would be applied to the opinions of others towards the would-be cross-disciplinary expert described the question, but perhaps it could be applied to the would-be expert's opinion of him- or herself.