It seems the music track doesn't trigger from the latest texture, but from the underwater texture. There are usually two types of water: water created by the level (which isn't a texture, so the music comes from the seabed texture), and water textures used to create rivers, lakes, and shallows. This is similar to lava and swamp, although the ability to walk on lava can be disabled.
You can also assign a separate track to the swamp; it seems to exist in the resources as Terrain-Swamp.ogg, but it isn't used, and the water track is played instead.