Djokovic will remain locked in a Melbourne hotel that also houses refugees until at least Monday when his legal challenge against his visa cancellation and deportment orders continues in the Federal Court.
He was joined on Friday by Czech player Renata Voracova with the ABF also rescinding her visa in the same circumstances.
The doubles specialist, who had already played in the Australian Open warm-up tournament in Melbourne this week, is set to return home and not challenge the decision.
Federal Court papers released on Saturday revealed a positive COVID-19 test on December 16 as the basis for Djokovic's medical exemption.
The world No.1 received a letter from TA providing a medical exemption on December 30, while the papers also include a partial transcript of an interview with an Australian Border Force officer on arrival that states "you are not vaccinated against COVID-19".
TA hasn't commented publicly since the Djokovic debacle began late Wednesday night, but Tiley sent an internal video to Australian Open staff saying that the team had done "everything they possibly could".
Leaked to News Corp, the tournament director said he was unable to speak publicly due to the pending legal action.
"We've chosen at this point not to be very public with it and simply because there is a pending lawsuit related to entry into Australia for a few," Tiley said.
"Once that has run its course, we'll be able to share more with you."
Two letters sent by the Department of Health in November to Tiley reiterated that unvaccinated players couldn't use a COVID-19 infection within the last six months as grounds for a medical exemption when entering Australia.
News Corp also published an information sheet sent from Tennis Australia to players last month.
The letter outlined the grounds for medical exemptions for vaccinations, including a COVID-19 infection in the last six months, again at odds with the advice TA received from government authorities.
But TA rejected that players were knowingly misled, and Tiley said organisers had followed "instructions".
"A lot of finger pointing going on and a lot of blaming going on, but I can assure you our team has done an unbelievable job and have done everything they possibly could according to all the instructions that they have been provided."
Praising staff for their work Tiley appeared to have no thoughts about quitting the tournament boss post he has held since 2006.
"I'd like to congratulate and thank the team that have enabled over 2500 players and their staff to get into Australia," he said.
"However unfortunately over the last couple of days, there's been a circumstance that relates to a couple of players, Novak particularly, in a situation that is very difficult.
"We're a player-first event, we empathise with the situation we currently have, and are working closely with Novak and his team and others who are in this situation.
"We're going through a difficult time in the public arena right now (but) we'll pull through it, we'll get out on the other side," he said.
Despite international condemnation of the handling of Djokovic, Tiley said new additions to Melbourne Park meant visitors would consider the 2022 tournament the best they'd attended.
"For fans coming on to the site they are going to see things and experience things they've never had before, and I want to make them come back next year," he added.
"We're going to deliver an event that people are going to say '2022 was the best event I've ever been to'."
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