Volume 3 of the Aldnoah.Zero Blu-rays came with a collection of four short narratives about Inaho and Yuki's life well prior to the events of episode 1.
In the second of them, 「春の遠足」 "A Trip in Spring", we learn that Inaho, Yuki, and their mother had been on a train to somewhere when Heaven's Fall occurred. Their mother was killed immediately, probably because a meteor landed near their location (though the story is mostly told from Yuki's point of view, and she, being five-ish years old at the time, obviously doesn't have the best recollection of events). Somehow or the other, Inaho and Yuki both survive, and she, carrying Inaho, follows the crowd of evacuating people, eventually ending up in an underground shelter afterwards.
Their father, a military man, was deployed at the time; a short while after Heaven's Fall, while Inaho and Yuki are still living in the shelter, Yuki receives a letter from the government indicating that they have been deemed war orphans. The implication being, of course, that their father, too, is dead.
The Saazbaum hypothesis is clearly implausible.