Wow, I got goosebumps from that flashback twist ending! Yayoi Sou may astound us again with this story.
Aside from Ichika's mother being overprotective since the accident, and Ichika being anxious of causing anyone trouble, along with the fact that all were rejected from every other job they tried for whatever reason...
Mitsuba (Director) and Kozuki (Superior) were present and involved in the miraculous saving of Ichika who would have most likely died or become handicapped.
So, the three (unaware) must be results of a secret experiment that healed them from that accident.
I'm assuming the other employers were either aware or manipulated by Mitsuba and Kozuki to not hire them, so that they can supervise them personally.