The French veteran felt Federer's reputation meant he was granted his preference to play in the evening session to avoid the blistering Melbourne heat and offered the Swiss' matches at the last two Australian Opens as evidence.
Federer will face South African Anderson in their final group match on Thursday.
The Japanese world number nine looked poised to end the season on a high after taking the scalp of six-time victor Federer in their opening round-robin match at London's 02 Arena. I can't talk about what would come next because it's a hard match in itself. I guess it was my head.
"I am very happy that I showed a reaction after the last match", said Federer, who will attempt... "He deserved that win at Wimbledon but hopefully I'll get my revenge".
Anderson, the first player from his country to qualify for the ATP's blue riband tournament since 1995, leads the Lleyton Hewitt group with two wins after trouncing Nishikori 6-0 6-1.
Thiem, the Austrian world number eight, was relieved to break his duck at this year's Finals following straight-sets defeats by Anderson and Federer.
Roger Federer has hit back at claims he gets "preferential treatment" from tennis tournaments due to his status as one of the sport's all-time greats.
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Thiem saved a break point in the opening game but at 1-1 he sent a forehand long to give Federer the advantage he never really looked like relinquishing.
Both will enter this one with points to prove, but Thiem needs to put in the performance of a lifetime and hope Anderson crushes Federer to have any realistic chance of progressing.
'It feels good, ' said the 37-year-old afterwards.
The inspired 32-year-old won the first 11 games but was denied only the second "double bagel" in the event's 48-year history after Federer's 2005 rout of Argentina's Gaston Gaudio. "I was playing very, very bad".
"My first-round match here wasn't great, so today was better, and I need to keep that up against Kevin, obviously, if I want to have a chance to stay here in London".
"I got off to a really good start and I think I did a really good job constantly applying the pressure and not letting up".
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