  There have been recent debates about whether $\overline{\text{MS}}$ parton
densities exactly obey positivity bounds (including the Soffer bound), and
whether the bounds should be applied as a constraint on global fits to parton
densities and on nonperturbative calculations. A recent paper (JHEP ${\bf
\text{11}}$ (2020) 129) appears to provide a proof of positivity in
contradiction with earlier work by other authors. We examine their derivation
and find that its primary failure is in the apparently uncontroversial
statement that bare pdfs are always positive. We show that under the conditions
used in the derivation, that statement fails. We provide some elementary
calculations in a model QFT that show how this situation can generically arise
in reality. In addition, we observe that the methods used in the derivation are
in common with much, but not all, other work where factorization is derived.
Our examination pinpoints considerable difficulties with these methods that
render them either wrong or highly problematic. The issue of positivity
highlights that these methods can lead to wrong results of phenomenological
importance. From our analysis we identify the restricted situations in which
positivity can be violated.
