As you noted... If you have the tests done and pre-empt the requirements then you have demonstrated your duty-of-care.
If you have not had a management plan / risk assessment, then I suggest it is responsible behaviour on the part of our government to intervene and ensure the safety of the greater population ("The needs of the many outweigh the needs of the few - or the one" Spock) by ensuring an individual poses no additional risk.
If this results in a required change of career then so be it...
And Government departments have been sharing personal information for decades - I've been involved with/in such systems... If medical information is shared eg. to licensing and the relevant medical statements to confirm the person is safe to operate machinery/plant/equipment then I see no problem with that.
As long as the information is used under controls to prevent improper manipulation...



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