I'm not defending interview quiz-time, but it isn't (or shouldn't be) about rolling your own solution. It's about understanding concepts. Understanding the basics of time/space complexity are pretty fundamental when designing systems.
Developers frequently encounter hashing and (probably less-often) trees, so I don't see an issue with asking something like "Why/how/when is a hash-based lookup faster <in some situation> than a tree-based lookup?" (as one question during an interview). If a person can give a good answer to this, they'll pretty easily be able to understand the performance tradeoffs of hash vs btree indexes when using mysql (and this same tradeoff in a variety of other situations).