  Nematic superconductors are characterized by an apparent crystal symmetry
breaking that results in the anisotropy of the in-plane upper critical magnetic
field $H_{c2}$. The symmetry breaking is usually attributed to the strain of
the crystal lattice. The nature and the value of the strain are debatable. We
perform systematic measurements of the $H_{c2}$ anisotropy in the high-quality
Sr$_x$Bi$_2$Se$_3$ single crystals in the temperature range 1.8~K$<T<T_c\approx
2.7$~K using temperature stabilization with an accuracy of 0.0001 K. We observe
that in all tested samples the anisotropy is weakly temperature dependent when
$T<0.8\,T_c$ and smoothly decreases at higher temperatures without any sign of
singularity when $T\rightarrow T_c$. Such a behavior {is in a drastic
contradiction with the prediction of} the Ginzburg-Landau theory for the
nematic superconductors. We discuss possible reasons for this discrepancy.
