Another said Turei was so popular within the party's membership that a resignation would have caused a "meltdown" at a critical time - just before an election.
The idea of a co-leader outside Cabinet is not a foreign concept to the Greens. In its planning for Government, the party has proposed such a role to keep an eye on backbench MPs.
Co-leader James Shaw backed Turei yesterday, saying that "everyone is entitled to a past".
Her decision to forgo a ministerial role appeared to be partly influenced by new Labour leader Jacinda Ardern, who said that she would not have been happy having Turei in a Labour-Greens Cabinet.
Ardern's comment had the potential to test the Labour-Greens relationship, but a Green source said there were no hard feelings toward Labour yesterday. The Memorandum of Understanding between the two parties remains intact.
Turei ruled herself out of a Cabinet position after coming under pressure over new revelations about her past as a solo mother on the domestic purposes benefit. She revealed that she was once registered to vote in an electorate she was not living in so she could vote for a friend, and that she was living with her mother while she was on welfare - though she claimed the two were financially independent.
While the new claims were no more serious than her admission last month that she might have committed benefit fraud, they gave the impression she had not been completely up-front. The ongoing controversy also threatened to overshadow the left-bloc's new-found momentum following Ardern's selection as Labour leader on Tuesday.
Turei insisted yesterday that New Zealanders could still trust her, and that there were no more skeletons in her closet: "I have nothing more. This is it."