Runtime of Grover's algorithm
The question is usually taken to be moot, for the following reason.  Grover's algorithm is a combinatorial search algorithm to find a solution to an arbitrary predicate.   While, yes, $\Theta(\log N)$ is the quantum gate complexity in each stage of the black-box algorithm, the predicate needs to be computed too.  The quantum gate complexity of that is $\Omega(\log N)$, because otherwise it wouldn't read the whole input and you could discard some of the input bits from the search.  On the other hand, an interesting predicate could take a lot more time than that.  Hence, the number of calls to the predicate is taken to be the standard coin, just as it is for the classical analogue of Grover's algorithm, namely random guessing.