Umm, while the copper side is in fact labeled "BAT" in your above picture, what you have pictured is the main circuit breaker, not a relay...
To answer the OP, I've often wondered about this myself as it doesn't seem to matter. On the relays that can be spun, printing right side up or upside down doesn't seem to affect operation of the bike. Best I can figure, the pins are paired diagonally. Thus, when you spin it around 180 degrees, the direction of the current flowing through both the coil and the switched side is technically reversed, but the pairs remain the same. I'd test this to confirm my theory, but don't have access to my bike at the moment.
'04 Kingpin - Blue w/ Tribal Flames (sold)
'12 Cross Country - Imperial Blue