  We present a critical examination of the recent article by Waclawczyk et al.
(2014) which proposes two new statistical symmetries in the classical theory
for turbulent hydrodynamic flows. We first show that both symmetries are
unphysical in that they induce inconsistencies due to violating the principle
of causality. In addition, they must get broken in order to be consistent with
all physical constraints naturally arising in the statistical
Lundgren-Monin-Novikov (LMN) description of turbulence. As a result, we state
that besides the well-known classical symmetries of the LMN equations no new
statistical symmetries exist. Yet, aside from this particular issue, the
article by Waclawczyk et al. (2014) is flawed in more than one respect, ranging
from an incomplete proof, to a self-contradicting statement up to an incorrect
claim. All these aspects will be listed, discussed and corrected, thus
obtaining a completely opposite conclusion in our study than the article by
Waclawczyk et al. (2014) is proposing.
