Ah yes indeed. One big BG it is. I wonder if the problem goes away if it's made of lots of BG objects? Probably will... but I don't know if I could be arsed with that :/
But if you are just using one large BG tile then the problem goes away of your texture is a power of 8. Like, if it were 128x128 or 256x256 then it would be okay for that purpose. But tiles that are separated would still have that problem, as I showed in the example above.