Today I noticed on an 1881 Japanese map (大日本府県分轄図), which I previously posted HERE, that Japan's Oki Island (隱岐) and Matsushima (松島) are marked in the same brown color, but Takeshima (竹島) is not marked. A region near Oki Island on the Japanese coast is also outlined in the same brown color as Oki and Matsushima. If the 1881 mapmaker believed Takeshima to be Korea's Ulleungdo and Matsushima to be Liancourt Rocks, then that would probably explain why he marked Matsushima as Japanese, but did not mark Takeshima. (Mr. Tanaka Kunitaka talks about the map HERE.)
The positions of the islands on the map suggest that its Takeshima was the mismapped Ulleungdo (Argonaut), and Matsushima was the real Ulleungdo, so the mapmaker seems to have colored in the islands based on their names and not on their positions. The real Liancourt Rocks do not seem to appear on the map.
CLICK ONCE ON THE MAP TO TO ENLARGE IT AND AGAIN TO ENLAGE IT MORE