In my experience, high-pressure "fix it now" scenarios are about leaning on what you know about the system, interpreting metrics and log messages, understanding how it's going wrong, and deploying a (usually very simple) fix. Sometimes just blindly hitting the "rollback" button as a first step fixes it, too.
Performing well in this kind of scenario is much less about algorithms and data structures, and much more about systems thinking and the level of your understanding of your system.
Both of you have points, but I absolutely agree with this. Outside of "Healthcare.gov goes live tomorrow and turns out it's completely broken" scenarios I've never seen something that would require a ground-up design and build of a system under emergency production time constraints.
System knowledge and knowing which one bolt to replace or turn is almost always more effective.
PS: Not to mention, if we're getting into algorithmic complexity levels of engineering on a monkey patch to a production system, then so many alarm bells are already ringing.
Performing well in this kind of scenario is much less about algorithms and data structures, and much more about systems thinking and the level of your understanding of your system.