Unless he is very clear (in context OP does not provide) to point out which senses of the words he is restricting his discussion to, Stephens is wrong in that he is not acknowledging the wide range of shades of meaning associated with each of these two words. They are synonyms (ie the ranges of their accepted meanings overlap). Though most people would agree that the 'centre of gravity' of the 'worried' range lies markedly closer to the 'anxious' side of the continuum, and that of 'concerned' somewhat closer to the 'not willing to turn a blind eye to' side.
The ODE definition is inadequate in that it implies that worry/trouble/anxiety must accompany concern; zeal to right a wrong / help sufferers may be the controlling factor.
The correct way to sort out the semantics here is to try to pinpoint the sense intended (enervating / debilitating / crippling worry; compelling concern) though then immediacy is lost. Perhaps pragmatics make the original preferable, but one has then to point out the at least partly subjective usage to be fair to understandably puzzled readers such as OP.