I just replied about that after stumbling onto this article days too late haha. Having worked in and around secure facilities for a long time, getting visitor badges and being escorted around doesn't require much.

It wasn't HYDRAs camera. It was just a random

Because he wasn't specifically looking for THAT information. He was looking for ANYTHING he could use and found that information.

Visitor badges, even at TS facilities, do not have pictures on them. You get your visitor badge and your picture ID checked against the access roster, then you are given access. It also never says anything about them knowing or trusting him, just that he was sent for. Working in government, I can tell you that the…

All of SHIELDs and HYDRAs data got dumped to the internet at the end of Winter Soldier. He poured through it trying to find anything he could that would help him destroy the Avengers. They literally explain this in the movie. But you know, piss on plot points you didn't pay attention to instead.