I'm guessing that the Asami thing came out of left field and running away shortcutted the twin's family story because it was intended to leave the game's actual story unspoiled. The resolution of that plot hole you point out is the prize for playing the game. Asami's mysterious "darkness" mentioned on the website is probably something else altogether that isn't being explored in the anime.
It is a shame the anime decided to come up with their own story when their own writers sucked.
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There's not that fine a line between willing suspension of disbelief and something just being stupid.
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