The broadcaster allegedly implied that the Government had mismanaged international aid donations. The Attorney General complained that breached accuracy and fairness and Campbell Live viewers were given an inaccurate impression of post-tsunami spending.
Mr Hodder said the complaint was serious and the BSA "went wrong" by not getting further information, despite the complexity of the case.
Lawyer for the authority Andrew Scott-Howman told the court the primary responsibility of the BSA was resolving complaints.
Last financial year it dealt with 250 of them.
Sarah Bacon, representing TV Works, said thousands of informal complaints were dealt with by broadcasting networks in-house.
The authority rarely, if ever, held formal hearings and its response to complaints was prompt, Mr Scott-Howman said.
But the prospect of formal hearings was considered at board level "on occasion," if sought by a complainant or broadcaster.
Mr Hodder argued that the BSA should have held a formal hearing, seeking further submissions and more information when the Samoan Government case proved wider and more complex than the usual complaints. And it should have admitted "we do not think we can determine this."
He added: "I don't think this should happen in very many cases, but when there are the kinds of issues that this complaint raised, it should."
The judge questioned whether the authority's current resources and time constraints would allow extra investigations.
BSA operating costs are around $120,000 a year, about half of which is funded by New Zealand broadcasters.
Justice Williams has reserved his decision on the Samoan appeal.