Arabia is the only civ with a desert start bias. Oil spawns in the following terrain types: desert, tundra, snow, marsh, jungle and coast, making it probably the rarest of the strategic resources on land tiles (though it occurs more often than horses if you count the coastal oil), as there isn't much marsh or jungle on the map and nobody settles snow. The civs with tundra or desert start biases (Russia and Arabia, respectively) are pretty much destined to end up as oil barons, which one can only assume is intended.
It is possible for Arabia to end up with no oil, but really pretty unlikely. Getting more is a bonus, but not that much of one in single player. In MP, it is more meaningful as you're likely to have a couple of civs that are hurting for oil, as landlocked plains/grassland civs often draw no oil or end up fighting over a single marshland/jungle source.