It's her job to matter of fact follow protocol no matter what, or how many times. The employees there are living double lives often, supreme liars in doing so, so of course you're not trusting anyone in that context, ever. And being surprised is not an option, thus the gun!
What you see (and have seen) is what you get and have!

I was just thinking that it's because someone could've been wearing a disguise to look like them. Her hand was on the gun until their identity was verified by retinal scan and palm print?

She knew Harry and Tom Arnold already because they work in the same agency but that doesn't mean that they couldn't have flipped to a different agency.

I think we were meant to see that the security here was so tight they weren't taking any chances , and although the movie doesn't really have an example of it , maybe they expected the possibility of some Mission Impossible like face mask $h#

Wow, you must work there? Cool!
What's it like?

She's "that cautious" because she's been ordered to be "that cautious". It's her job.
"It ain't dying I'm talking about, it's LIVING!"
Captain Augustus McCrae

I'd say it was for the viewer's benefit, to let us know that the Omega Sector's security is some serious ****. That and she's just following procedure. No matter how redundant it may be, she'd have to follow it every single time someone walks in if she wants to stay employed there.
"Wasn't Einstein German?"
"Hard to tell from his accent, Russ."