The DPP can't
investigate allegations. It has no investigative powers. The Police have to do the leg work.
That's why the allegations are already before the NSW and Victorian police. FWA has the power to investigate the HSU, it does not have the power to investigate whether an individual has committed an illegal act. I would have thought Chief Justice Brandis SC (given that appellation as a political manouevre eight years after he ceased practice - the man is a monstrous legal lightweight) would have known the police forces of the relevant jurisdiction have that power. Then they refer the matter, where apprpriate, to the DPP by way of a brief of evidence.
If you think this is a bungle of the government's making, guess again.
AFAIK Ms Jackson, whose husband used to travel with Mr Thomson in his days working at the HSU, referred the matter to FWA.
As for Thomson, he has always maintained his innocence. Idiot Brandis, whose cross-examination and forensic skills are those of a dead sheep, and his acolytes think this means Thomson has denied using the card. That is not so. He has denied using it improperly or illegally - that is, contrary to any guidelines given to him by his employer. If no guidelines as to the use of the card were issued, that is the end of the matter. Kaput. No more. He will not be charged.
All of the above is within the public domain and pretty well known.
There's a lot more to this, but it cannot be said by me on here. Suffice to say much of it stems from two groups within the HSU who essentially control different factions within the union and who don't get on.