In their defense, the station has been taken over by a Vorta, and the Vorta aren't exactly known for being hugely trusting. I think we should be lucky that DS9 isn't under a Founder. At least with a Vorta, you might have had a chance at convincing her of the truth. A Founder would've called bullshit as soon as the first words left Kurland's mouth.
...Why oh why couldn't it have been a Weyoun clone? Weyoun may have been a dick at times, but he was also reasonable.