The remit of the inquiry is to examine abuse of children in formal institutions, such as children's homes. Crucially while that will include homes run by churches, the inquiry will not cover abuse in more general faith settings.
The latest voice to object to this limitation comes from churches themselves. The Churches Child Protection Advisory Service, a Christian charity based in Kent, but also registered in Scotland, says this is simply letting churches off the hook.
Instead, it says, the Scottish Government should have adopted the methodology currently being employed by the Australian Royal Commission Inquiry.
Abuse, it says, is just as likely to have occurred at churches in settings such as Sunday services. Paedophiles often seek out places of worship, CCPAS argues, as they are seen as a soft touch.
Simon Bass, chief executive describes it as a serious omission. "The Australian approach is highly relevant, for it has since 2013 been hearing extensive evidence of incidents of abuse within institutions," he says.
"But it is also taking evidence of abuse perpetrated by members of church denominations themselves - and how they have responded to those disclosures. Churches have therefore had to give evidence and explain why they acted as they did."
It makes no sense at all to excuse churches in Scotland from the same scrutiny, he adds. "In both places they are established institutions where, sadly, abuse has flourished in the past."
One of the reasons ministers have given for not throwing the net wider is the need for a clear remit and prompt findings. So it is maybe slightly contrary for Mr Bass to have added: "We are also concerned that the Scottish Government's four year time frame for the inquiry may be too tight to investigate all the evidence fully".
The inquiry has generally been welcomed, though, as has the government's plan to lift the time bar to allow victims to bring civil actions over historic cases.
Norman Dunning, chair of the Public Awareness Advisory Group (PAAG) for Child Protection in Scotland, said: "Everyone has the right to be protected from harm and we are encouraged that this inquiry will lead to greater protection of children in the care system in the future."
And despite some reservation, groups such as In Care Abuse Survivors (Incas) appear ready to give the inquiry a chance. Nevertheless, pressure to extend Ms O'Brien's brief may continue to grow.