But thats exactly i'm thinking too. That there would be an investigation and they would get busted.
Busted ? I'm not sure at all. Remember the state of the Vanguard. It wasn't ready for the mission and was re-equipped in emergency. This led to absurdities like some monitors being placed upside down. And before the IA became crazy, Annie was still trying to fix many problems. She just have to overload the right card in the console and it's done. There were a shortcut somewhere, and before the card was totally burnt, making the cannon out of order, it goes random and fired few bullets.
Who will question this, when the lost guy had to goes outside precisely because of another malfunction ? If it was the only problem, I agree, they would have been busted. But here it's just one over many. And don't forget that the investigation will take place only when they'll return. At this time, they'll also have many things to report regarding the station, things that will need to be investigated deeply, whatever because of incompetence, madness or conspiracy. When you face a situation that can question the whole colonization process, and eventually end it, you don't care about the loss of one guy ; especially when the said colonization process is already massively questioned on Earth.
In fact, I even see them going further : "Has terrorists gone too far ? Their sabotage of the Vanguard, one of Intrepide's ships, endangered an emergency rescue mission and killed a man. It could have been your son that was killed, your parents that needed to be rescued, can you still support them and sleep well at night ? The debate after few ads". Then, as first ad, I see an, "engage in the space fleet, become the last hope of our colons, become a hero !", or a, "they need you ! Our colons needs you to protect them, to rescue them. They need you to sleep tie at night, knowing that whatever can happen, you'll be there to save their day".