Paediatrician David Southall must wait to learn if a High Court Judge will rule he should be removed from the medical register.
Professor Southall arriving at the High Court
The Council for Healthcare Regulatory Excellence had challenged a General Medical Council decision not to have Professor Southall struck off.
He was found guilty of serious professional misconduct last year.
Professor Southall had accused the husband of Sally Clark of murdering his two sons after seeing a TV documentary.
The High Court judge is to announce his decision in several weeks.
Sally Clark, from Wilmslow, Cheshire, was convicted in 1999 of murdering her two sons Christopher and Harry.
But that conviction was quashed when new medical evidence showing the babies died of natural causes was accepted at a second appeal hearing in January 2003.
The GMC hearing centred around conclusions Professor Southall drew after seeing an interview with Mr Clark on Channel 4's Dispatches programme broadcast in April 2000.
In his interview, Mr Clark described how the couple's first baby Christopher had suffered a nosebleed just 10 days before he died in December 1996.
Professor Southall told police he believed Mr Clark had killed the children after watching the interview, but without seeing any documents relating to the case or interviewing the family.
He later outlined his concerns in a report. It was submitted to the family court, which was considering who should take care of the Clark's third child.
The Clark family has called for the doctor to be removed from the register.
During the High Court hearing, Monica Carss-Frisk QC, for the CHRE told Mr Justice Collins the penalty was "manifestly inadequate and inappropriate".
She said the GMC had "woefully failed" to "maintain confidence in the medical profession and send out the right signals to the public".
Ms Carss-Frisk added that Professor Southall still maintained "to this day" that the view he reached based largely on the television programme "is still right".
She added: "He has at no time offered any apology or shown any insight, remorse or contrition".
The CHRE believes the only appropriate penalty is to erasure Professor Southall's name from the register of medical practitioners.
But the GMC says striking off was not the only option.
Mark Shaw QC, appearing on behalf of the GMC, defended its Professional Conduct Committee's decision not to "sacrifice" Professor Southall's "distinguished and outstanding" career as a paediatrician - despite his "Achilles Heel" in the field of child protection.
He said: "I am not prepared to accept that erasure is the only possible sanction."
But Mr Justice Collins suggested Professor Southall's stance revealed "arrogance".
"He has a belief, and he believes he is right, and he forms his belief on less than full material and he will not be swayed whatever the consequences".