The 47-year old Williams, who had caddied for Woods since 1999, was dismissed by the former world No. 1 last month. Woods had said earlier this week that the discussion took place face-to-face on July 3 after the final round of the AT&T National, where Williams had caddied for Scott for the second time while Woods was injured.
"That is incorrect," Williams said shortly after Scott's four-stroke victory over Rickie Fowler and Luke Donald at the WGC-Bridgestone Invitational. "I was told on the phone that we needed to take a break. At the AT&T, the details of the firing were discussed."
Williams suggested that Woods was not happy when he asked permission to caddie for Scott at the U.S. Open, which Woods was skipping due to knee and Achilles injuries that kept him from playing tournament golf for three months.
"He didn't agree with it and thought it was time to take a break," Williams said. "I was told on the phone that we needed to take a break. And in caddie lingo, that means you're fired. Simple as that."
Woods' agent, Mark Steinberg, disputed Williams' version of the story, saying first in an email and then later by phone that the firing did not take place until July 3.
"Tiger flew from Florida to Philly to visit AT&T National and also for the express purpose of PERSONALLY and officially telling Steve that they would no longer be working together," Steinberg said in the email. "Tiger felt strongly about meeting face to face. Any assertions to the contrary are simply false."
Asked specifically if Woods dismissed Williams when the caddie asked to work for Scott, Steinberg said no.
"Steve might have thought things were not going to work out, but it did not happen until that Sunday,'' Steinberg told ESPN.com by phone.
Woods, who tied for 37th at the Bridgestone in his first tournament without using Williams since 2005, was asked on Tuesday if he told Williams face-to-face.
"Yes, I did,'' he said. "We had a nice conversation. We did it after he completed play at AT&T National up in the boardroom, and it was a tough conversation, but we said what we needed to say to each other face to face and man to man.''
Williams said that he and Woods talked at the AT&T National, but it was simply to discuss details. According to Williams, he had been fired at some point previously after seeking permission to caddie for Scott.
Williams, who lives in New Zealand, said that the win with Scott was his 145th as a professional caddie. He has caddied for Scott at the U.S. Open, AT&T National, British Open and now the Bridgestone.
"It's been the most fun thing,'' he said. "It's the greatest week of my life caddying, and I sincerely mean that.''
Bob Harig covers golf for ESPN.com.