Theoretical defects of MWC

[osobliwy nick]

I'm reading:

https://pcg.di.unimi.it/pcg.php

and prof. Vigna wrote there:

"The generators above pass all statistical tests, but have a few theoretical defects, which are partially fixed by a generalized version defined by Goresky and Klapper: GMWC128 and GMWC256."

I looked at the paper:

https://www.math.ias.edu/~goresky/pdf/p1-goresky.pdf

and they wrote there:

"However, Tezuka et al. [1993] and Couture and L’Ecuyer [1994] discovered the remarkable fact that these ´ vectors lie very nearly on the lattice of vectors formed by the associated linear congruential generator with base b, multiplier B, and modulus m."

So is this a problem that Vigna referred to or there is something else? By the way is PractRand able to detect lattice structure? Probably not directly, because there is no such a test in this battery? So generator with such flaws can pass all the tests, but still have a lattice structure, am I right?