He only asked for permission to videotape yellow-badges leaving the building. Nothing more. Unless someone wants to show me where I am missing a statement, I don't see any point at which he even claims that he was given permission to film and interview employees - much less about the issues he has taken it upon himself to "investigate".
That it was done on his own lunch break and supposedly using his own tape doesn't seem very relevant. My free time is my own, but my company wouldn't appreciate it if I was using my lunch time to bother my employer or one of their clients.
From the video/transcript: "Eventually I asked a superior on my team if I could borrow a camera to go out in the parking lot and videotape the yellow-badged workers leaving the 3.1459~ factory."
If he had asked permission to take a camera out and videotape interviews with people leaving the building so he could investigate the socio-economic aspects of Google employment of Google's ScanOps team, I think it is safe to say that his employer would have told him to STFU and get back to his actual work and there would have been no problems. He took advantage of the situation to push an issue his employers were not aware that he was pursuing which then put them and all of their other employees and their contract with Google in a tenuous position. Not necessarily because "ooh no, he's going to find out we have lots of people of a certain race working in that building", but most likely because they hired some guys to get a job done and not be a thorn in someone's side.