The unit, incidentally, was set up to investigate the veracity of statements by public figures - such as the Prime Minister's claim that the ABC regulates itself. In fact, it falls under the Australian Communications and Media Authority's remit.
As well as triggering a wider debate about the role of a free media, the row - stemming from the ABC's revelations last year that Australia spied on Indonesia, and its reporting of allegations of mistreatment of asylum-seekers by navy personnel - has highlighted divisions between conservatives such as Abbott and moderates such as his Communications Minister, Malcolm Turnbull.
Although Turnbull chided ABC managing director Mark Scott over the spying story, he defended the organisation this week, telling Fairfax newspapers it was accountable to its board and should not be dictated to by politicians, although the latter "will often be unhappy" about what it broadcast. It's hardly a secret that Turnbull, who has also spoken out in favour of same-sex marriage, still harbours leadership ambitions. A Roy Morgan poll this week gave the Coalition its lowest ratings since the election, with it six points behind Labor on a two-party preferred basis.
The other aspect of Abbott's hidden agenda, many believe, is to divert attention from the Government's clandestine border operations and, effectively, to shut down reporting of asylum-seeker issues.
Sceptics rolled their eyes when he declared the media "ought to be prepared to give the Australian Navy and its hard-working personnel the benefit of the doubt". Not so Miranda Devine, a Daily Telegraph columnist, who believes claims asylum-seekers suffered burns when navy personnel forced them to hold on to a radiator are "uncharacteristic of Australian culture and inconsistent with 100 years of Australian military history".
She must have forgotten about the claims of sexual abuse within the military, including the navy, which prompted six separate inquiries by the previous Government and a formal apology to victims by then Defence Minister Stephen Smith.