Photo courtesy of David Backlin (taken December 2004)
Missouri 43 and Oklahoma 43 really don't run concurrently along the Oklahoma-Arkansas border, as this sign assembly suggests. Arkansas 43 and Oklahoma 20 do run concurrently for about five miles until reaching the Missouri border near Southwest City.
There's more: the assembly also indicates that an Oklahoma route (20) is sharing the same road as an Arkansas route (43). "East 20" and "North 43" eventually do lead to Missouri.