Jack said she had never heard of Ligandrol - a prescription-only drug used to increase muscle mass - let alone knew how to pronounce it, but believed it was found in "contaminated supplements".
Horton told the Seven Network on Sunday night, however, that his position on the topic "remains firm".
"I was disappointed to learn late yesterday that a fellow Dolphins team member had recently returned a positive A sample," he said.
"I applaud the decision to immediately withdraw the athlete in question from further competition until this matter is resolved."
Tensions erupted early last week during the opening night of the World Championships in South Korea after Horton, who came in at second place in the 400m freestyle, refused to share the podium with Chinese swimmer Sun Yang as he was presented with the gold medal.
"His actions and how it has been handled speaks louder than anything I could say," Horton said at the time, referring to doping allegations levelled at the athlete.
Sun, a 10-time world champion, was accused in 2018 of destroying vials of his blood that were due to be taken for drug testing.
The Chinese athlete, who had also served a three-month doping suspension in 2014, was not punished by FINA for smashing the vials because the drug testers did not show adequate identification.
"Clean sport must be a priority for all athletes, all sports and all nations," Horton added, following Jack's revelation.
'I believe in Shayna'
Jack's coach Dean Boxall has also addressed media regarding the failed test, telling the Sydney Morning Herald that he believed his athlete would be cleared.
"She's going to fight and we are going to fight with her and Swimming Australia is going to fight with her. I believe in Shayna. I believe strongly her story," he said.
"This is a very, very sad story."
On Sunday, Swimming Australia CEO Leigh Russell said she felt "distressed" watching Horton's protest while knowing about Jack's failed test, which had not yet been made public.
According to Ms Russell, a confidentiality agreement between Swimming Australia and the Australian Sports Anti-Doping Authority (ASADA) prevented the organisation from revealing the results earlier.
Instead, 20-year-old Jack was sent home from the team training camp citing personal reasons. She later said she was planning on disclosing the news to her teammates after the World Championships so it wasn't a distraction.
"I absolutely support Mack. He's entitled to say and do on an issue that he is passionate about and we are too, this has not changed our thinking on a zero-tolerance approach or our policy," Ms Russell said on Sunday.
Australian team head coach Jacco Verhaeren said he believed that given knowledge of Jack's results, Horton would still have protested Sun's medal.
"If the meet started tomorrow with this knowledge he would stand there again and if I could I would stand next to him," he said.
"This is about someone standing up for clean sport and we still do that."
Jack is at home in Brisbane and is being supported by Swimming Australia.