It sounds like something that is happening at the moment and there is an element of shock or surprise. "He's eating chocolate?" "He can't be eating chocolate he hates it?"
In this case, both να φάει and να τρώει are correct. "Αυτός δεν μπορεί να φάει σοκολάτα is an alternative translation. ^.^
(Usually, when it comes to Subjunctive in Greek, the difference lies in the continuation of the action. If the action is continuous, Present Subjunctive (να τρώει) will be used. If it isn't, Past Subjunctive (να φάει) will be used (of course, the characterizations Present and Past do not indicate time periods. Duration is what makes the Subjnctives distinct).
In this case, it is not clear if the action is habitual or not in English. So, both are accepted. ^.^)
Red-screened today: He mustn't eat chocolate. Really? Even though μπορώ can mean "may," as well as "can"?
If what you mean is that "mustn't eat" was the sentence shown as correct we'll need a screenshot on that, because what we have is "cannot" or "can't". There is no "mustn't' or "must not" in the incubator for this sentence.