The DUP's William Humphrey made the claim after saying he had spoken to the man who returned the statue to Father Gary Donegan at Holy Cross Church.
However, a similar statue of the Virgin Mary was photographed at the Lanark Way bonfire last year. The religious icon was placed halfway up the bonfire, beneath an Irish tricolour.
But the SDLP accused the North Belfast MLA of "unfettered ignorance" and Sinn Fein said his party was "making it up as you go along".
There were loud jeers when Mr Humphrey, who interrupted Ulster Unionist leader Mike Nesbitt, said: "The icon was thrown into the bonfire at Lanark Way by people from Divis in the lower Falls."
As shouts rose, he added: "It is factual. I spoke to the gentleman who returned it, and he took it to Gary Donegan. That was the conversation."
The SDLP's Conal McDevitt responded: "We enjoy a certain degree of privilege in this House, but we do not enjoy the right to show such unfettered arrogance and be so abusive and insulting."
As Speaker William Hay twice demanded "order" and accused MLAs of abusing procedure, Sinn Fein's Gerry Kelly asked Mr Humphrey to explain how, if the statue was thrown on the bonfire, in photographs it was clearly sitting upright on a plinth.
"You are making this up as you go along," he added.
Fr Donegan, the parish priest of Ardoyne, who said it seemed that the statue was only on the bonfire at Lanark Way for 10 minutes before it was removed, said he believed "hoods" from both sides of the divide had swapped stolen cars and the statue was left in the car afterwards.
"The important issue I have to emphasise is that it was a very generous decision to return it and a very brave decision to return it," said Fr Donegan.
The face of the statue was missing and it had two major cracks along with scorch marks on the back. Fr Donegan added: "I used it as a symbol to preach about peace on Sunday and then some volunteers took it away to get it repaired.
"This incredibly responsible act proves that there are leaders within our communities who remain committed to taking positive steps for peace."
The Assembly exchanges came after Mr Nesbitt said: "A religious icon was stolen and placed on an Eleventh Night bonfire. I will make it clear that that was not done in my name.
"I deplore that act, and I acknowledge the clear hurt that will have been caused in the Catholic community.
"I understand that there was some sort of gallows on a bonfire that has been taken as a reference to a well-liked and popular priest who took his own life recently.
"That was not done in my name, and I acknowledge the deep hurt in the Catholic community over that.
"I deplore all sectarian acts, including the attacks by nationalists on Orange halls that have taken place recently, and the burning of the Irish national flag."