As a person who works on a large enterprise network, it's highly unlikely that they have a single button capable of shutting things down. A large-scale commercial venture like this would likely have multiple redundancies and failovers in place to prevent a single-site issue from taking down the entire thing.
If this truly is a software issue somewhere, the engineers would need the back-end systems to continue running in order to troubleshoot and correct the issue, so the answer would likely be to shut down routes in the front-end DMZ routers and/or firewalls to prevent access from the outside. And then hopefully they have some way to VPN in outside of these front-end network components, or a bunch of software guys are going to have to head on-site to fix this.