Well, considering they weren't concerned and thought that she left of her own accord, you're right ... they didn't bother to investigate.
Exactly, someone leaves a note saying they're going UA, so why would they investigate? It's not an uncommon occurance, I can assure you. They were not informed of much of what civilian LE was finding out, just as civilian LE was not informed about what military authorities knew. I bet the sheriff's department usually gets total cooperation from units that they contact, so it didn't occur to them (except Sheriff Brown) to contact higher ups.
In my opinion, the horrible communications problems can be directly laid on the unit level. The sheriff's department says they kept trying to contact the unit and got no return call. Sounds like Laurean or a buddy took care of that. His first sergeant and his CO were extremely poor judges of his character, or he would have been in pretrial confinement. The car keying and the punch in the face would also have been handled at the unit level, if they were reported at all.
I think the authorities in Lauterbach and Laurean's unit had a preconceived notion that Lauterbach was the unstable one of the pair. Even her mother seemed to perceive her as somewhat unstable. What nobody picked up on was that Laurean was completely evil, and was most likely planting the seed all along that she was an unreliable, hysterical drama queen in the minds of his workmates and their unit commanders. There's no excuse for the unit to have fallen for this ploy. They should know their soldiers better than this, especially the first sergeant should have.
I don't think the higher military authorities on base are covering anything up. They are just stating what they knew and when they knew it.