> For Groover algorithm, which is applied to the problem of search you can prove that there is no classical algorithm faster than O(N) - looking at each item in the worst case scenario.

Assuming that you cannot "look into the black box of the oracle" (i.e. we are only allowed to use a given oracle to evaluate an item at an index).

You still have the case of a list of perfect random numbers. There is nothing in the box then.

But perfect random numbers cannot be evaluated by an algorithm. Evaluating the black box/oracle must be done in a run of Grovers's algorithm.