A provision requiring all persons opening non-resident accounts to swear affidavits which would then be available to the Revenue was dropped from the 1983 Finance Bill following protests from the banks.
The measure was modified by the then Minister for Finance, Mr Alan Dukes.
Fianna Fail had wanted the section of the Bill dropped in its entirety.
The chairman of the Revenue Commissioners, Mr Dermot Quigley, referred to the amendment of the provision when he was questioned about the AIB controversy by the Dail Committee of Public Accounts on Tuesday.
In 1983, the then Fianna Fail spokesman on finance, Mr Michael O'Kennedy, described Mr Dukes's proposal as a "crazy notion" and said that contacts in the banking community had told him that it had already caused people to take money out of the Irish banking system.
During a Report Stage debate, he said non-resident depositors feared that the fact of their having deposits in Ireland would become known to the Revenue authorities in the US and Britain, who would be informed by the Revenue here.
Mr O'Kennedy, who said there was £1.4 billion in non-resident deposits at the time, wanted the measure deleted rather than amended and said Mr Dukes's amendment placed "an impossible burden" on the banks.
Mr Seamus Brennan (FF) said he was aware that at least one of the major banks had privately estimated that up to 50 per cent of the money in non-resident deposits was at risk if Mr Dukes's proposal was not amended.
"The rest of the Finance Bill is just mickey mouse stuff compared with the ramifications and implications of this section," he said.
Mr Gay Mitchell (FG) said at the time the measure was aimed at residents who opened non-resident accounts.
"It is alleged that this is a common practice," he said.
He said the attempts by Fianna Fail deputies to oppose every section of the Bill at Report State as well as at Committee Stage would get them no thanks "from the worker or from the man in the street. Probably the only people who will thank them will be those with funds to invest in political parties".
Mr Dukes said the section "is an anti-evasion section to deal with the problem that has been identified and has been known about for some time".
He said he would amend it "in recognition of the importance of the psychology of the market and in recognition of things said from the opposition benches here and in the banking community". The amended section stipulated that non-resident depositors would not normally be required to produce an affidavit.
They would make declarations of non-residence to the banks and, if the bank was not satisfied with the declaration, an affidavit would be sought. This is the current situation.