"I haven't said anything as we are working on the issue," noted BioWare community coordinator Chris Priestly in response to countless complaints (no really, countless complaints) on the official forums. "I understand you are all irritated by this, but we want you all to play, so we are working hard to determine and fix whatever is causing this."
Update: Priestly has created a new thread tracking the issue. Apparently, the original download was corrupt and prevented "all" PC users from playing the new content. That file has since been removed from BioWare's download section (though it's harmless if you did download it). "We are working on a fix for the issue and will get a working file up for PC users ASAP," Priestly assures, without knowledge of a more specific ETA.
Update 2: Priestly delivers the good news: "Lair of the Shadowbroker should now be fixed for the PC and should be able to be downloaded now for both the PC and Xbox 360."
[Thanks, Killer rin & Daniel]