The couple, who cannot be named, have come under heavy criticism for apparently rejecting the boy, Gammy, at birth and taking only his healthy twin sister back to their home in Bunbury, south of Perth, from Thailand.
The surrogate mother, Pattaramon Chanbua, has insisted she will raise the seven-month-old child after saying the biological parents at first requested an abortion and then walked away when they learned of his condition.
But the Australian couple said in a statement, issued through the friend to their local newspaper the Bunbury Mail, the allegations were false and they did not know he had Down's syndrome, although they were aware he had a congenital heart condition.
"Gammy was very sick when he was born and the biological parents were told he would not survive and he had a day, at best, to live and to say goodbye," the friend, a woman, told the newspaper, without saying who told them this.
The birth of the twins was supposed to take place at a major international hospital in Thailand but Ms Pattharamon went to another facility, which made the surrogacy agreement void, according to the newspaper.
This meant that the couple had no legal rights to the babies although the surrogate mother finally agreed to hand over the girl, the report said.
"The biological parents were heartbroken that they couldn't take their boy with them and never wanted to give him up, but to stay would risk them losing their daughter also," the friend said.
She added that allegations that the couple "ignored" Gammy when they visited the hospital were untrue and they had bought gifts for both infants.
"They prayed for Gammy to survive but were told by doctors that he was too sick, not because of the Down's syndrome but because of his heart and lung conditions and infection."
The friend added that the couple spent two months in Thailand but due to military unrest at the time felt they had no option but to leave without Gammy.
"This has been absolutely devastating for them, they are on the edge," she said.
- 'I have never lied' -
The case has sparked fevered debate on the moral and legal grounding of international surrogacy.
Commercial surrogacy, in which a woman is paid to carry a child, is not permitted in Australia but couples are able to use an altruistic surrogate who receives no payment beyond medical and other reasonable expenses.
To avoid those curbs, Surrogacy Australia said couples are increasingly choosing to find women willing to carry their baby overseas, with several hundred each year travelling to India, Thailand and the United States.
While the full picture of exactly what happened remains unclear, Ms Pattaramon insisted to AFP on Tuesday she had been transparent.
"I have never lied or hidden anything. The truth is the truth, it's up to society to make their own judgement," she said.
Ms Pattaramon has said she agreed to carry another Thai donor's egg fertilised by the Australian man, reportedly aged 56, in exchange for around US$14,900.
An agency, which she refuses to name for legal reasons, acted as the go-between.
She says the agency told her the parents wanted her to have an abortion once medical tests revealed the boy had Down's syndrome, but she refused.
Abortion is illegal in Thailand -- except in very specific cases including rape and to protect the mother's health -- and it also runs counter to beliefs in the overwhelmingly Buddhist kingdom.
Thai health authorities say it is also illegal to pay for surrogacy and someone who agrees to carry a baby must be related to the intended parents.