The children,Lahala,6,and Noah,4,were snatched off the street last Wednesday by several men. Ms Faulkner was working with the British-based firm Child Abduction Recovery International. Lebanese authorities reportedly have some evidence that60 Minutes paid the $115,000 fee to the firm.
The botched operation follows Ms Faulkner's separation from the children's Lebanese father Ali Elamine,who took Lahala and Noah to Lebanon and,according to Ms Faulkner,refused to let them return to Australia.
"What they did in the Lebanese law is called kidnapping. They had the intention to save the kids but they are at the same time kidnapping them,"the police source.
Equally there would be an understanding that Ms Faulkner was acting as a mother in what she saw as the interests of her children,the source said.
"Looking at it from an emotional perspective,you need to see how she was thinking."
The60 Minutes crew,who accompanied Ms Faulkner,clearly"acted out of excitement".
"There's a difference between kidnapping for ransom or kidnapping to return kids to their mother. So in this case their judgment will be minimal. It's not going to be extreme,"the source said.
"I don't think they'll stay (in detention) for too long. I think they'll be released soon."
The source added that"there's one Romanian who hasn't been found yet - he fled".
It was not clear whether he was still in Lebanon or had escaped the country.
The snatching happened on the streets of southern Beirut,which is controlled by Shiite political factions.
Complicating the issue,Mr Elamine's family is reportedly politically connected. His mother,Ibtisam Berri,who was knocked aside on the street during the snatching at a school bus stop,is the cousin of Lebanese parliament speaker Nabih Berri,according to reports.