The maxim is that you cannot achieve security through obscurity, where security offers some guarantees (mathematical, physical, etc.). Obscurity, while offering little to no guarantees, can certainly be a quite useful part of your protection plan.
There is a reason people don't go around wearing their credit card numbers and SIN on their clothes. The system to protect them should be setup to work its best in the scenario this information is completely exposed but our attempts to hide his information does add a tangible benefit.