Illegal move on Rapid Chess Tournament

Hi,

During a Rapid Chess Tournament FIDE (25 min + 10"), with a strong position, under 3 min, on an illegal move, the arbiter, behind me, said "game lost" !! without the intervention of my opponent who autorized me to replay.

We were under "inadequate supervision" ! one arbiter for 16 tables.
Article 14 A4 is very vague ...

Was the arbiter right ?
Need for truth, thanks.

no move is illegal until your opponent claims it. The usual treatment of the illegal move is adding some time to the your opponent. 

I thought the games were reverted to before the illegal move?

They are, however only players are allowed to claim illegal move, 3 fold repetition, clock flag etc. Nobody is allowed to participate in the game except the two players. 

if one of the players claims illegal move, he calls arbiter who then checks it and reverts the move, add time to clock etc.

Thank you for your answers. I understand also that the arbiter has to add time (2min) in all situations, (adequate supervision and inadequate supervision)

I suppose that why they call them arbiters and not refrees..