This golden rule states that if in a group play, team or individual A beats the close rival B but both finish atop of the group and advance, when they meet again in the final, B will beat A. There are exceptions, but it happens often enough to merit evaluation.
The rule requires a competition format in which the field is composed of two round-robin groups, and then the elimination stage. If you have a single elimination format or a single, large group, then nobody has a second chance. If you have many groups, common in football, then title contenders are never placed in the same group. Another limit for the rule is that A and B must be close in their world ranking, level of play, win-lose record, etc. Thus, it does not apply to the US basketball teams and other clear favorites.
Not many tournaments use this format. The most high profiled ones are the Olympic volleyball and tennis year-end championships. Below are examples of A and B play in the group stage as well as in the final.
1984 Olympics. Men, US lost to Brazil in group 0:3, but won the final 3:0. Women, China lost to the US 1:3 but won the final 3:0. These teams finished the groups as #1 and 2 and were considered strong title contenders at the time.
1992. Men, Brazil beat Netherlands 3:0 and 3:0 twice. However, Netherlands was #4 in the group and considered a surprise getting to the final.
1996. Men, Netherlands vs Italy, 0:3, and 3:2. They finished their group #1 and 2.
2000. Men, Russia vs Yugoslavia, 3:1, 0:3. #2 and 3 in their group. Women, Cuba vs Russia, 2:3, and 3:2. #1 and 2 in group.
2004. We have the true exceptions this year. Men, Brazil vs Italy, 3:2, 3:1. Women, Russia vs China, 0:3, 2:3. All finished #1 and 2 in group. But on the women's side, Cuba was considered a stronger team than Russia, and Russia actually came awfully close to winning the final.
2012. Men, Brazil vs Russia, 3:0, 2:3. #2 and 3 in the group but had the same 4:1 record as the #1 US. Russia came back from two sets down but the fifth set was easy, unlike the Chinese women in 2004. Women, Brazil vs US, 1:3, 3:1. US and Brazil rank #1 and 2 in the world. Brazil was #4 in the group but only because of the upset by a clearly weaker South Korea team.
This rules is not limited to volleyball. In ATP tour championships, 8 top players are placed into 2 groups, and top 2 advance to the SF and final. In both 1994 and 1996, Sampras lost to Becker by a close 0:2 but prevailed in the final 3:1 and 3:2. Becker was then still a dangerous player, able to beat Sampras enough times, and in 1996 playing in Germany the match was like a heavy weight title fight.
Why loser (B) of the first match tends to win the second time? Because it happens so many times, it can't be attributed to the randomness of sports. Perhaps B wasn't in the top form during the less important group play, or B made adjustments after the loss, to which A failed to adapt.
So if I am B going to the final, I will feel confident but still need to figure out what went wrong the first time. If I am A, I will be very alarmed. Expect B will be very different, motivate myself or the players, and mentally plan for dramatic changes in the process and strategies.