I am rewatching DS9 for the second time. I just watched 'the sound of her voice'. Not sure why I didn't even notice the first time (or remember), but why did they not know until they went to the surface that she was already dead?
Wouldn't it be standard procedure to check the status of the ship she claimed to be on that crashed? With all the crazy stuff in Star Trek universe there are always imposters, changelings, etc... it could be fraud.
But also, & more importantly, to update the status of the ship. Or rather, whether it was reported missing, or if not to report that it is currently in distress, & that it crashed and has one survivor. I'd think Starfleet would like to keep up to date records on everything (especially during war). We do irl. Our militaries do. Even normal businesses do.
I'd think the first moment they get a distress signal they'd check it's validity & update it's status. A few earlier episodes ago "Valiant", they got a distress signal & Sisko immediately knew it's status (off the top of his head though because it was a little more important being a high end war vessel much like the defiant).
In fact, my memory of this episode was wrong (or mixed up with some other Star Trek episode all together) based on this very reason. I thought they figured it out and told her, then went to the surface merely to get her body. I remembered this episode totally wrong because of this very thing.