So I wonder - why should an agent be related to a specific user's credentials? Is the right way to go about this is to create a "fake user" for the sake of the agent?

Very true you have to have credentials for the trains-agent, so it can "report" to the trains-server, that said, the creator of the Task (i.e. the person who cloned it) will be registered as the "user" in the UI.
I would recommend to create an "agent" user and put it's credentials on the trains-agent machine (the same way you add any credentials), this way you do not "bleed" credentials throughout the system.
WackyRabbit7 , Make sense ?