During multi-disiplinary sporting events (such as the Olympic Games), there are two ways to present the medal table: rank the countries/teams by gold medals or by total medals. (Countries are ranked by the latter in North America since at least the 1990's while they are ranked by the former in most other countries.) For most of the just-concluded Olympic Games in Tokyo (officially called the 32nd Olympiad), China won the most gold medals while the US won the most medals overall. On the last day the US won 3 golds to take the top spot in the gold medal count as well.
Naturally, there are Chinese who don't accept the results and move on. They created a "final" medal table where China won the most gold medals once more, by adding the ones won by Hong Kong and Taiwan (Chinese Taipei) to China's total. Their justification is that both Hong Kong and Taiwan are part of the People's Republic of China. (It is true for the former; the latter, not so much.)
With that logic, the EU can also claim that it should be on top of the gold medal table (by adding all the gold medals won by its member states.) The US can claim Puerto Rico's medals as its own. Likewise for the British by adding the ones won by Australia, Canada, New Zealand, Jamaica, Kenya and the rest of the Commonwealth to its medal haul. If China, the US, Britain and the EU can add medals this way, the EU would take over the top spot. The medal table (ranked by gold medals won) would look like this:
| Rank | Country | Gold | Silver | Bronze | Total | 1 | EU | 85 | 94 | 109 | 288 | 2 | Great Britain | 74 | 60 | 92 | 226 | 3 | China | 41 | 38 | 27 | 106 | 4 | United States | 40 | 41 | 33 | 114 |
Zealous Chinese patriots would rejoice over finishing above the US, but their blood would boil when they see that China finished a distant third to the EU and, worse, Great Britain.
If we take this arguement further, Britain can also include the medals won by the US in its medal count. Mongolia may argue that, since the China was under Mongol's rule during the Yuan dynasty, it should be the country with the most gold medals. The Italians can also lay claim to the title, as they may claim the gold medals won by countries that used to be (fully or partially) occupied by the Roman Empire as their own, while France may count the gold medals won by countries that used to form its empire. Meanwhile, Japan and Germany can add the gold medals won by countries they used to occupy during World War II to their column. If we count medals that way, the medal table would, based on my 15-minute research, look like the folllowing (igonoring the fact that there would be overlaps between nations):
| Rank | Country | Gold | Silver | Bronze | Total | 1 | Roman Empire | 129 | 154 | 184 | 467 | 2 | Great(er) Britain | 113 | 101 | 125 | 339 | 3 | Japan | 97 | 89 | 86 | 272 | 4 | EU | 85 | 94 | 109 | 288 | 5 | France | 85 | 88 | 97 | 270 | 6 | Germany | 82 | 95 | 120 | 297 | 7 | Mongolia | 80 | 98 | 91 | 269 | ≥8 | China | 47 | 42 | 45 | 134 |
So the Romans (Italians) would come out on top in this competition, winning the most gold, silver and bronze medals (and over 100 medals ahead of Great(er) Britain). The exercise shows that if a country tries to artificially inflate its medal count, make sure this won't boost the medal count of other countries by a greater extent. (Zealous Chinese patriots may then resort to count all medals won by ethnic Chinese towards China's total.)