But these algos are developed during months or years of research, team meetings, white boarding and experimental prototyping.
These things are not developed under the pressure of a ticking timer (well, technically there is the time constraint, but usually the limit is more than 30 minutes).
Also, the problems are very palpable and concrete and the drive to solve them is much stronger than in an interview, where the anxiety of failing the interview hangs over your head.
Basic CS/Math/AI/Physics knowledge affords you a starting point that's further along in the development/tweaking of an algorithm. That is NOT the end point. Its simply - knowing whats out there.
If you start with "well let me go read about whats out there" you will only have time for superficial knowledge from wikipedia or what have you. Because that starting set of knowledge takes years to accumulate. Testing whether you have this starting set is a crucial setup in knowing whether a candidate is going to constantly end up wasting time reading up on basic stuff. You can't build a plane by opening a high school physics book.
One other thing is that when you have a broad enough set of domain knowledge in your head, its much more likely that you're able to connect the dots cross-domains. This is essential if you're going to be doing some interesting algorithmic work.
Of course, all of what I said is predicated upon you being interested in that sort of work.
More than likely you'll be working on a team, where you need to understand some of these concepts, and you'll grow in to them. Almost every single person on that team did not come in off the street with expert knowledge in those domains.