I reloaded the game you mentioned and combed through the log to see when opponent gained/played Distant Land. He had bought it 4 times, but only played it 3 times.
This confirms the 'easy' check when hovering over opponent's information area on your last turn, which also shows that he has 3 Distant Lands on his Tavern mat.
The result you saw at the end game screen seems to be a quirk. If no Distant Lands are on the Tavern mat, they seem not to be listed at all (I created a short game where I bought one and then resigned). If there are however Distant Lands on the Tavern mat, *all* Distant Lands in a player's deck seem to be listed under the '#' column. I created a game where I bought 2 and resigned after playing *1*. Here the end game screen showed 2 Distant Lands in the '#'-column, but correctly only 4 points in the 'VP' column.