Judge Robert Spear said Siddiqui will reappear on August 31.
However, he said he would entertain a bail application if he was supplied further information.
Judge Spear uplifted the suppression and declined bail as there was a "need for openness in the pursuit of justice and there's no reason at all in my view of any significance that would justify continued name suppression".
Siddiqui's lawyer Kerry Burroughs told the Herald outside court that the police argument came down to one document - his physician and surgeon's licence issued by the State of Illinois.
The document doesn't state when it was issued but it expired on July 31, 2017. Mr Burroughs believed they lasted for either five or 10 years.
Mr Burroughs showed the Herald a copy of the certificate but wouldn't comment when questioned whether it was his clients or not.
He also couldn't comment as to why his client was in possession of, and used the document, if it wasn't his.
Mr Burroughs said his client - who was "stressed" about his current position - had been living in the United States since at least 1992, which was when he was issued his Degree of Philosophy from the University of Arizona.
Siddiqui also had a Degree in Psychiatry and Neurology, from 2011, issued by the American Board of Psychiatry and Neurology, and his Degree of Doctor of Medicine issued by the Medical University of the Americas, in the West Indies, dated May 23, 2008, that were not being contested by police.
Mr Burroughs claimed that suspicion about his client seemed to stem from an email he sent to his superiors on July 12 stating that he had concerns for patient's safety.
However, again, Mr Burroughs couldn't go into detail about his client's claims as he was yet to see the email and the Waikato DHB had not yet disclosed it.
Mr Burroughs was dubious of the DHB's sudden reversal of his client's skills when, after a four month review by his supervisor in May, he received "exceeds expected standard" in most areas of his work, including clinical knowledge, diagnostic skills, time management, recognising limits, professional knowledge, reliability and professional manner.
Mr Burroughs said his client told him that once he sent that email - on July 12 - his professional career began to crumble as the next day his supervisor decided that he no longer wanted to work with him. As Siddiqui requires supervision at all times, it meant that he could no longer work until the DHB found him a replacement. He sought legal assistance from Mr Burroughs last Tuesday before visiting him again on the Thursday.
Siddiqui's two children - a 20-year-old son and 18-year-old daughter - have also been holidaying in New Zealand and were present when the police carried out their search warrant on Friday, July 24.
Siddiqui's estranged wife is living in America.
Mr Burroughs said Siddiqui decided that as he could no longer work he would head back to India to see his mother who was critically ill.
There was nothing in his contract which stated that he had to give any notice before quitting, he said.
