James Clayton: All I know about the CIA is that they're a bunch of fat, old white guys who fell asleep when we needed them most.
James Clayton: Iwo Jima Memorial. This where you tell me about duty and sacrifice?
Walter Burke: No, this is where I have my breakfast burrito. (00:56:20)
Walter Burke: All right, your objective: Reach the parking lot with an asset who intends to have sex with you.
James Clayton: You want us to pick up a girl?
Walter Burke: Five, actually. One each.
James Clayton: Would I have to kill anyone?
Walter Burke: Would you like to?
Suggested correction: A good number of mice and keyboards connect to the computers through the USB ports. If they took out all but two ports, and left those for the mouse and keyboard, it could be possible. If Leila pulled out the keyboard plug she could put in the USB device and copy the files. Heck, she could have even opened the computer up herself and installed a hidden USB drive (smuggling in the tools with her coffee mug of course). She would just have to be sneaky about it, and that's nothing unusual for these characters.
Not only is the original "Corrected entry" valid, it's understated. Burke actually said "Langley's computers don't have disk drives" - not just no floppy drive. In a high-security environment, such a system would be configured so that no USB port could communicate with an external drive; even more likely, the workstations would be dumb terminals - just keyboard, mouse, and monitor; and that's exactly what they appear to be in Layla's office area. So, showing a USB port built into Layla's keyboard and communicating with a USB drive belies a major part of Burke's story, and if Layla were able to do that, the system would immediately "see" it. It's the ersatz "Correction" that's mistaken, since it describes only ordinary commercial computer systems.