A) Rape is not normally considered "amicable relations". It still produces children, so the lack of amicable relations between Chinese and Mongols is no barrier to cross pollination.
2) Regarding the "arbitrary." selection of these four individuals. I believe they were more likely chosen for their fame than for any other reason. They could as well have chosen Ifituti the slave girl, Wing Fat the rice farmer, Pierre the swine herd and Daoud ibn as-Sakkhrah the waterwheel operator but nobody ever heard of them. They also didn't say that Nefertiti was an ancestor of Confucius (although at just under 1000 years it's not impossible*) any more than they would be saying that your maternal grandmother is a descendant of your father's paternal grandmother, merely that you are a descendant of both.
*With the more conservative figure of four generations per century we have 10 to the 12th slots for ancestors a thousand years ago. Obviously many of these are going to be filled by the same person but it leaves us a lot of room for outsiders.
