Note that there are two different versions of Mersenne Twister PRNGs being discussed in the documentation: MTGP32 and MT19937.
The way I read it, the first quoted remark seems to apply to MTGP32, but I agree this is not entirely clear. I note that the CURAND documentation also says: The MTGP32 generator exhibits some marginal results on “BigCrush”.
Consider filing an enhancement request with NVIDIA to get the description clarified. Use the regular bug reporting form and prefix the synopsis with “RFE:” to mark it as an enhancement request.