RIO DE JANEIRO—During the opening round of beach volleyball at the Rio Olympics, the Brazilian star Alison Cerutti reacted to a call from the referee by whipping off his own hat and chucking it to the ground.

All eyes in the stadium turned to the chair above the net and the trim, baseball-capped figure of Roman Pristovakin, a 38-year-old Russian making his first appearance at the Olympics.

Mr....