Exactly. This is sort of a stretch of a metaphor here, but consider the predator having a server system that provides an API. The ground station is just a client putting out requests to that API. The ground station computers had the virus. That whole series of articles in the press was kind of stupid. If I use github, have a virus on my computer, it doesn't mean that github has a virus on their computers.
Yes, in this case though the virus was apparently a keylogger on a system that isn't (supposed to be) connected to the internet. So while it may have gathered information on what the operators typed in, it wasn't getting any magic passwords. Most of that (if done properly) would involve some secret keys that operators don't directly access.