Published reports said Adams, the doctor who performed cosmetic surgery on Kanye West's mother shortly before she died this month, was previously sued for malpractice and arrested for drunken driving.
Authorities in Los Angeles are investigating the death of Donda West, who died of complications from the surgery and who was buried Tuesday, the same day Adams was slated to be interviewed on King's show.
Adams appeared after the first commercial break and politely told King he would not speak, TMZ.com reported.
"I had come here to talk about things in the press that aren't accurate about me. But I have a tremendous amount of love and respect for the West family and they've asked me not to go on," he said before taking off his ear piece and walking off the set, prompting King to go to commercial.
Alan Tenenbaum, Adams' attorney, later explained the doctor received a letter from attorneys representing the West family asking him not to appear on the show.
Notable deaths of 2014 [PHOTOS]
Polly Bergen, Emmy Award-winning actress, dies