In Latin, approximately, it's meaning as a layman is retained - but when it reached English it came to mean a dullard and eventually took on a medical twist (anyone with an IQ under 30).
The -idi part refers to a "private" or "singular" "alone" (note, the lowest rank in the military is a private soldier). And so the idiom is simply a private exchange, an exchange that can only be understood when the parties involved are in on the joke. When the Pilgrims first used the term "nose to the grindstone", they were in fact refering to working hard to produce corn flour.
Is it any wonder that foreigners have such difficulty with idiomatic English when most native speakers haven't a clue about the original meaning - and perhaps care no further than acknowledge a collection of words, jumbled together with an agreed meaning?
And so to the downfall of the idiot. The original term was not considered an insult by the Greeks, merely a factual statement about class. It really took off as a insult when it reached northern Europe, and flowered alongside the growth of industrialisation. Of course the process of industrialisation requires workers; and the workers required specialisation for industry or agriculture.
Perhaps like the word "nice", idiot has come full circle and come to mean it's opposite. Post-industrial countries no longer need the tradesman-for-life; general skills are in order, as you might find that job you invested all that time and money training for being contracted out to India.
So Mr Fox has finally figured out Mr Hedgehog's one big trick. And you wouldn't call Mr Fox an idiot, would you?
All the best, Victor.