What is unreliable? Captain's airspeed? F/O's airspeed? Standby Airspeed? All three systems have independent sources of pitot and static data. If one significantly disagrees with the other two, then you would assume that the disagreeing one is faulty.
The Captain uses the #1 ADIRU as a source for airspeed, the F/O uses the #2 ADIRU. The left pitot probe feeds the #1 ADIRU. The right pitot probe feeds the #2 ADIRU.
The air data fed to the transponders depends on the ALT SOURCE switch on the ATC panel (assuming all ATC panel models have this switch). If the ALT SOURCE switch on the ATC panel is in "1", the #1 ADIRU supplies the airspeed data to the ATC. If the switch is in "2", the #2 ADIRU supplies the airspeed data.