  Two recently published papers (J.D. Barrow and A. Paliathanasis, Eur. Phys.
J. C. (2018, 2019)) claim to have found exact solutions of Einstein's field
equations belonging to the class of non-trivial Szekeres models, whose source
is a mixture of dust and a homogeneous time-dependent scalar field, where the
energy-momentum tensors of both mixture components are independently conserved.
We prove that the independent conservation of these two mixture components
necessarily leads to solutions belonging to the set of spatially homogeneous
subcases of the Szekeres family: Friedmann-Lema\^itre-Robertson-Walker for
class I, and Kantowski-Sachs, Bianchi-Behr I or Bianchi-Behr
$\mbox{VI}_{\tiny{\mbox{-1}}}$ for class II.
