If someone draws a map and it has some streets with the wrong names, you say, "This map is not accurate." It doesn't mean you are talking about something numerical.

In this case accuracy is appropriate :)

Accuracy is about how close to the underlying behavior that is being modeled is. In this case, the goal is modeling the controllers they are using.

Precision is about how stable I can make my controller parameters and how stable they can make the behavior or the underlying fusion.

What they did was changed the fidelity of the model. Rather than parameterizing it using a known controller model (e.g., a PID controller) they used the neural network to fundamentally discover the important parameters that they can understand and how they interact.

The simulation can be accurate or not accurate entirely independently of how much fidelity of the actual phenomenon you model. You need to have a high fidelity model, and that model needs to be accurate, and they behavior needs to be precise and stable.

An example would be how wing profiles in aircraft are simulated/modeled. I can do it in 2D with high accuracy and high precision - it's a GOOD 2D simulation. But its low fidelity. I might be better off with a lower accuracy model of a high fidelity model, like a 3D model that lets me look at how the ends of the wingtip perform as well. Increasing the accuracy of that model might make the results less stable (because numerical techniques...great). A lot of improvements in computing power and simulation techniques have resulted in the ability to simulate systems more completely and learn about the interactions - not just making the simulation more accurate to what it contains.