Its quite simple. Tiled backgrounds render in a special way such that the uv co-ordinates wrap instead of clamp. So when a tiled background is rendered at a decimal place co-ordinate, the texture interpolation is grabbing colours from the right. You notice this something in low quality 3d games when people accidentally setup the wrapping incorrectly and you get trees that have a semitransparent line above them etc.
This isn't necessarily a bug in some situations. If you have a tiled background that is a seamless texture, you expect the texture in calculated the interpolated pixels, to account for the pixels that are wrapped on the other side of the image.
Ultimately when it comes down to it though...why are you using a tiled background for these tiles which you dont actually want to tile at all? The tiled background object is really for images that you want to repeat over and over again.