I have absolutely no familiarity with your agency specifically or Fire/Rescue in SA in general, but if you would find it helpful I can give you a few reasons which would be pertinent in the US.
1. Training. Recreational buddy rescue and Public Safety Diving are very different animals. Without getting into the Haz-Mat issues, you need to be able to run a repeatable, verifiable, and tight pattern in zero visibility. This is nigh impossible without using a line (jackstay or tended pattern) and connecting multiple patterns is best done with shore support. Your first task is not to rescue the victim; your first task is to find the victim. If you are in rescue mode, you can then bring the victim up; but you need to be able to cope with any entanglement issues during the search and rescue, including extricating the victim from a vehicle. If you are in recovery mode, your responsibility shifts to properly documenting the scene, preserving evidence/chain of custody, and respectfully returning the victim to the surface (preferably already in a body bag). Unless your recreational rescue class deviated considerably from the usual standards, I doubt all these points were covered.
2. Credentialing. In a criminal trial, because of your role in the recovery, you may be called to testify. Without the proper training, the integrity of your evidence is in question. Without the proper training, if you are injured or die during a dive, your organization may be civilly or criminally liable. They are certainly morally so.
3. Safety. PSD is a team animal. The only way in which to ensure a fast, safe response is for each member to know and trust the others; working in parallel. Without a team, you are a liability; not an asset. If your department has a team, even if you had the proper training, you would need to train with them to build that trust and learn the game-plan. If I walked up to you at a structure fire and said I was a firefighter, would you let me pack up and take the nozzle?
4. Liability. Simply put, this is a dangerous business. Your department may not want to deal with the liability and expense of a team.... and certainly not with that of a lone wolf splashing with no back-up.
I have no idea what your specific agency's policies and reasoning are, but these are a few common reasons. I'd be happy to answer any additional questions about them, but remember: nobody at your agency gives a hoot about whether I think you should be able to dive or not.
If you want the real answer, you'll have to ask your officer.
