I think a lot of confusion on this topic stems from what Google values from a candidate's knowledge of algorithms. From my experience, these technical interview of an algorithm, but you sure wouldn't have to prove anything formally.

Algorithm and computer science knowledge can be applied very practically. Skienn a also wrote a book called Programming Challenges, which features problems very similar to those asked in these technical interviews. The coverage of topics like dynamic programming may be very shallow from a theoretical perspective; however, an intuitive understanding and mastery of when to use the technique and how to write the code is absolutely crucial to solving many difficult programming problems.