Using the Babai's Naive Rounding algorithm to decode, in the conditions of the SIS problem, is secure?
The Nguyen-Regev attack on GGH and NTRU works because those schemes were "leaking" the trapdoor S while signing. So after observing a certain number of signatures, their algorithm could recover S. So their attack had nothing to do with solving SIS, but rather with how to use the leaked information to recover a trapdoor (which can then be used to solve SIS). In the regular SIS problem, the S is unknown to the adversary and there is of course no "leakage" coming from anywhere.