Legally, corporate security from other corporates should not lift a single finger to do anything on a rival corporation's territory unless explicitly asked to, even if it could mean letting people die. For example, if a Saedor Krupp security agent was witnessing a robbery happen at a NeoTrans transport terminal, they'd have to stay out of it unless authorized, or the corporation could and likely would attempt to prosecute them.
Why? Corporations see their own security teams as well-oiled machines that will do exactly what they need to do, unless unknown factors are introduced. Random rival corporate security intervening is not only vigilantism, but also could impede efforts from the correct corpsec team.
So, if rival corpsec team is authorized, then what? Authorizing third parties to intervene should be met with some pushback by higher-ups. It makes your corporation's security team look ineffectual, and can possibly make it look like a rival corporation saved the day on your own territory, a humiliating prospect.
I suspect the WJF also work much like this, but should also ignore corporate security threats even as they escape, unless explicitly asked to help, with the reasoning being that the moment the WJF gets involved the individuals involved in the crime cannot be handed back over to the relevent corporation. It is now business of the Hall of Justice, and if the corporation would like to buy any fines the WJF assigns, they can, but otherwise, the corporation is removed from the equation.
So, the WJF are authorized, what now? Well, like before, there should be pushback from higher-ups for relying on the WJF to handle threats to the corporation. If the criminals targeting the corporation are not handled by the corporation, the security team looks weak and they lose a chance to interrogate and privately punish the criminals their own way, or even indebt them to do their own bidding (free of charge, as opposed to buying fines from the WJF).
Just some ideas I've been thinking about, I realize a lot of this isn't mechanical but rather, perhaps, cultural, but I don't think the Ideas board is strictly mechanical, either.