Also at a big 5. We've found that skipping reviews causes more problems than it solves in emergency situations. It's really tempting to bypass the process because you're sure you can fix it fast, but this mindset results in more missteps in aggregate.
If a couple minutes really makes that much of a difference you should probably page multiple people in from the start of an issue.
Generally speaking, your un-reviewed change isn't a "fix", but something to stop the bleeding. It might move traffic out of a problematic area, or disable an experiment that's leading to unusual metrics.
In other words, its a rollback, not a fix-forward. (and I'll note that where I work, these changes still need to be reviewed soon after they're submitted). I agree that all fixes should be reviewed before submission.
If a couple minutes really makes that much of a difference you should probably page multiple people in from the start of an issue.