I just don't understand if there is wire connecting the PSU to the component why would one company's wire not work. The only reason I could think of is that the clips are different.
Even if the clips fit, which the main PSU one doesn't, that doesn't mean those clips are wired the same way. These also aren't. So if you plugged them in you end up with the wrong voltage being plugged into the wrong line on the motherboard, and poof there goes your PC.
Assuming just one 6 pin connection with 3 12V and 3 ground. There's at least twenty ways to wire the socket. The best way depends on the PSU design and cable design.
Just as a guess for individually sleeved you'd want to match the motherboard socket so the cables aren't twisted, so you take extra time and effort both designing the PSU and the connections to mean that. In a normal one its probably easier or cleaner to do it differently. Say all the ground pins on the bottom.