I think we're confusing two things here.
The test is referred to as the "bridge officers test." It certifies that you know the basics necessary to pull a duty shift on the bridge. It is never stated that it confers upon you any particular rank automatically.
As has been mentioned here, Pulaski was a full commander, but she obviously had no interest in training to command a bridge watch. OTOH, Data was a lieutenant commander, but he was third in command of the ship and clearly commanded on many occasions.
My interpretation is this: If you are a command-track officer, then you learn bridge operations as part of your normal training and don't have to take a specific "bridge officers test." If, however, you are an officer who is not in the command track, such as sciences or medical, you can choose to supplement your training and take the test. I would also guess Picard simply thought Troi's passing of the test was a good time to also promote her to full commander, not that passing the test is what gets you to that rank.