Thanks for your question.
The advice of the UKBA's official at the airport is correct in my view. I am quite suspicious of immigration companies and if I were a lay person would always rely on an immigration solicitor if I had the choice.
A 3 year ban is quite a serious ban, it would be noted in his passport. As a guide I attach some policy guidance on overstayers which is obviously a much more serious offence that your husband's act (which I would not even classify as an offence, there is certainly no UKBA guidance on it):-
You will see that for the quite serious offence of overstaying and then leaving of their own accord an overstayer only receives a one year ban. You get a two year ban for leaving at the expense of the governement within 6 months of notice of removal.
Overstays are not permitted as the sole reason for the UKBA to refuse a spouses visa either and yours is much less serious than that.
He should disclose it in his application and submit a notarise witness statement confriming the details and stating that his attempted re-entry was simply as a result of his honest mistake and a misunderstanding of the visa rights of austrailan nationals.
To deny him entry on this basis would in my opinion be a breach of his right to a family and private life, so even if they did reject then he would have a very good chance upon appeal.
If this has been useful please kindly click accept so that I may be rewarded for my time. It will be gratefully received and you will be free to ask follow up questions.