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Very Unlikely

Here's the situation that hasn't been sitting well with me for a while. The problem that I have is mostly with the terminology. I would welcome any input from both players and directors.

You pick up a 9 count with a 5 card suit and after two passes you decide to open 1.

Your LHO overcalls 1NT, partner raises to 2, RHO bids 2NT which LHO alerts. You notice a glimpse of surprise on your RHO's face.

You pass and LHO bids 3 (now everyone at the table knows what's going on). RHO bids 3NT and my partner leads a .

Dummy puts a rather non-descriptive 8 or 9 count with Tx of . I call a director and explain that IMO there was miscommunication in methods between LHO and RHO (they both confirm that; LHO, a highly ethical player, volunteers that their partnership explicitly discussed this very scenario few weeks ago and agreed to play Lebensohl)  and, if my RHO intended his 2NT call as natural then 3 bid from his perspective should have a choice between 3 and 3NT and with a relative minimum and no club support pass of 3 is not only a logical alternative, but a bid most of the players would've chosen. 

Director asks us to conclude the play and declarer wraps up 9 tricks.

Director comes back, asks about the result and lets it stay. When I ask for the explanation he says that 3 is so unusual that it would've definitely woken RHO up even if there was no alert.

I poll few players of RHO caliber (~ 5500MPs) about 3 bid and they all say that 3 is an offer to play. Some have suggested that partner thinks that you're playing Lebensohl.

I go back to the director with an intent to appeal and he does not accept my appeal (he believes there was no UI). The exact wording was "it is VERY UNLIKELY that a player of RHO's class would take the 3 as natural, therefore the result stands".

Now, I understand director's reasoning (whether I agree or disagree with it doesn't matter). What I didn't understand was the use of the words "VERY UNLIKELY", which, to me is something not really quantifiable (unlike the word IMPOSSIBLE).

Is it 1%? 10%? 20%? What's the mark when it stops being VERY UNLIKELY and becomes UNLIKELY? Is UNLIKELY sufficient for the presence of UI or has to be MAYBE?.

Is this something that is universally accepted among directors (talking about ACBL land) and the methodology?

What's your view on that? Should there be numeric brackets  to classify those probabilities to make it formal?

The poll I created is based on the view that the 3 was very unlikely.

Edit: Added "other" option to remove the number of abstentions.

It is indeed "very unlikely", I would let 3NT stand
Although it is very unlikely, I would roll contract back to 3
I disagree with "very unlikely" (impossible or likely), I would roll back to 3
I disagree with "very unlikely" (impossible or likely), I would let 3NT stand
Other. Will explain.

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