As long as nothing's on physical or metaphorical fire, Cortana solidly respects the International Dibs Protocol when it comes to human partners (if nothing else), so she accepts whatever limited feed Theta's providing without pushing for more.

"They missed the power main. That's almost a shame. It would have taken care of at least one of them." Generating physically tangible holograms pulls a lot of power, and having that trying to get to ground from a hand down through the soles of the feet is the sort of thing that leads to death certificates reading 'cardiac arrest secondary to electrocution.'

"Okay, steal the line out from the camera and swap it for the one they cut. The connectors are standardized." In North's HUD, if Theta chooses to pass it through, the proper cable and where to reconnect it is highlighted. It would take a sim trooper to screw it up.