This sounds like total bullcrap; prove it.
Statistically, with no time to think about their choice, there is a tendency to pick rock subconsciously (~37%) and this is especially true for less experienced players. Scissors is the next most likely choice, falling at about the expected 33%, while less than 30% pick paper as their first choice. With this in mind, the two best choices are Rock to either win or stalemate, or Paper for pure chance to win.
With time to think about your choice, Scissors is selected almost 40% of the time, expecting that no one would dare pick Rock knowing how predictable it is, thinking they will in the worst case, stalemate. Rock is by far the best chance of outright winning a thought out 1 round game, while Scissors is the most likely to win or draw.
Rock Rock Rock is good for 3RR because it plays with the other player's expectations.
R vs R: Stalemate
The opponent subconsciously will want to play the hand that beats rock
R vs P: 2P wins
The opponent will expect you to switch over to paper or scissors, and will most likely therefore switch to scissors themselves
R vs S: 1P wins, game is a draw
OR
R vs P: 2P wins
Opponent expects you to switch to what beat your hand, chooses scissors
R vs S: 1P wins
Opponent expects you to switch on the third hand, and most likely stays with scissors because with the assumption of a switch, they have no reason to switch themselves
R vs S: 1P wins, wins game
OR
R vs S: 1P wins
Opponent will either switch to what beat them or stay the same
R vs R: Stalemate
Opponent expects switch, and most likely switches to scissors
R vs S: 1P wins, wins game
R vs S: 1P wins
R vs S: 1P wins, and wins game regardless of next result
And, just for ****s and giggles
R vs S: 1P wins
R vs P: 2P wins
2P has either caught on that it will stay the same, or expects a switch, both are about equally likely.
R vs P: 2P wins, wins game