Tradeoff Bounds for Halfspace Range Counting
Matoušek's stronger time bound is correct.

The proof of Theorem 6.1 (in the journal version) uses an indirection trick that reduces the space bound required for logarithmic query time from $O(n^d)$ to $O(n^d/\operatorname{polylog} n)$.  Intuitively, the trick is to cluster the points into subsets of polylogarithmic size, build a linear-space data structure for each subset, and then build a standard logarithmic-query-time structure over the subsets.  Plugging the improved space bound into  Matoušek's multi-level/tradeoff machinery—described in gory generality in the longer version of Agarwal's survey—gives Matoušek's form of the time-space tradeoff.  (In fact, the indirection trick is just a very careful application of the standard tradeoff machinery.)