The side are already in danger of blowing their World Cup bid after two defeats in the first four days of the tournament left their campaign in turmoil.
The 29-year-old made his mark at the 'home of cricket' by leading the Mahendra Singh Dhoni-led India to a famous Test win there in 2014, his first tour with the national team.
The 37-year-old eased past Argentina's Leonardo Mayer and will face either close friend Stan Wawrinka or Greek sixth seed Stefanos Tsitsipas for a semi-final spot.
South Africa were poor on Sunday. An abject display in the field saw half chances put down and too many runs to slip through porous fingers or between flailing limbs.
Sao Paulo's security secretariat would not provide a copy of the complaint to AFP, confirming only that one had been filed but saying its contents were classified.
Williams, who suffered her earliest Grand Slam exit since Wimbledon 2014, was given a standing ovation as she walked off Court Philippe Chatrier while sections of the crowd jeered her conqueror.
The Italians travel to Athens to take on Greece on June 8 and before hosting Bosnia in Turin three days later, and Mancini said the 28-year-old could only blame himself for not being selected.