The rule meaning in reality, as it stands today is simple: you can ONLY enter Asia twice if one of those entries is a transit without stopover between SWP and Europe; period. The other rule means that the moment you touch Asia you pay for it, stopover or connection makes no difference, you still pay.

The transit without stopover rule in NA is different. In NA the transit without stopover is between SA and another continent, so it can be SA to Europe or SA to Asia or SA to SWP.