Tolerance parameter of statistical query model and adaptivity
What you are saying is that given $N$ random samples one cannot simulate an algorithm that makes $T$ queries to VSTAT$(N)$. If the $T$ queries are chosen adaptively then one might need more samples (the best upper bound is $\sqrt{T} N$ samples). 
This is true but not an issue for the planted clique paper you mentioned. That paper is concerned with proving a lower bound against algorithms using VSTAT. Specifically we prove that any algorithm using a polynomial number of queries to VSTAT$(N)$ will not be able to solve the planted $k$-biclique problem for $N=\tilde{\Omega}(n^2/k^2)$ ($n$ is the number of vertices on each side). Answering even a single query to VSTAT$(N)$ requires $\Omega(N)$ samples so the lower bound reflects the difficulty of solving the problem with with $N$ (or less) samples.