Exactly.

It makes perfect sense to leave it off, the absence doesn’t prove she didn’t work there.

But, as you may have heard:

The absence of evidence isn’t evidence of absense

https://www.youtube.com/watch?v=jHhG9DbHbW0

It doesn’t make sense to act like she proved she worked there. We simply don’t know either way.

I really don’t get what’s hard to understand here:

It’s just something incredibly easy to prove, so I don’t see the point in saying she did if she didn’t.