Can you point me to the exact quote where this is said, plainly and directly? Because the new update both implies (very strongly, so strongly I think most readers would find it conclusive) that A) Kane and Olivia are not blood related, B) both Veronica - who seems to be one of the ones controlling the gambit - and Elena want Olivia to win, and that to win, she must have a male child with Kane. Dunno, the game itself seems to contradict you pretty thoroughly.
The premise is kind of silly, because a logical thing to do would be to have the 5 (maybe 6?) Karlsson sisters play their gambit and determine a winner, then frame Kane into prison or coerce him some other way so his sperm could be extracted and just use artificial insemination. But this is a fantasy/dystopian/porn game, so of course fucking needs to be involved. By the game's own internal logic, an Olivia/Kane sexual relationship seems very, very possible.