En passant capture the only legal move

I was playing in a short 15 minute tournament when there when there was a dispute between two players over their game. One player claimed that the position was stalemated, while the other one claimed that his opponent's only legal move was the en passant capture of a pawn. The player claiming that the position was stalemated was at that time in a rather disadvantageous position, and probably would have lost shortly. However, as the time limit was quite short, the moves had not been recorded, and there had not been any spectators. I can't provide a pgn of this game, but what should the arbiter do in this situation, as he himself had not seen the game and so cannot justify the en passant claim? Should the game be drawn, or should it be adjudicated? (Assume that because of time the game cannot be replayed)

First, as an aribiter/TD I would verify if both players agreed on the last move; the pawn move made allowing the en passant. If both players agree that move was the last move made then you have to follow the rules; Section 5.2 a of the FIDE Laws of Chess

The game is drawn when the player to move has no legal move and his king is not in check. The game is said to end in ‘stalemate’. This immediately ends the game, provided that the move producing the stalemate position was legal.

So if the position is agreed upon and en passant is the only legal move, then I would say it is forced.

The only thing that matters, in this case, is that the position on the board is accurate and both players agree it is accurate.

The en passant move was indeed the only legal move in the position, but the player in the disadvantageous position (being a sore loser) refused to agree, insisting that the position was drawn. What, then, do you do as arbiter, as there was nothing to validate either player's statement?

As stated the last move made....if both disagree then can only give a draw.

The player doesn't have to agree if the en passant is legal, he need only agree to what the last move in the position was. From that, the arbiter can determine if the en passant is allowable or not.