  The isoscalar single-pion production exhibits a broad bump in the energy
dependence of the total cross section, which does not correspond to the usual
opening of the $N^*(1440)$ production channel with subsequent pion decay. In
arxiv:2102.05575 it was interpreted as a narrow Breit-Wigner structure, which
leads in a sequential single-pion production process to a possible explanation
of the $d^*(2380)$ resonance. We demonstrate that such an attempt fails
already, when confronted with the data base for isoscalar single-pion
production. We investigate whether the observed bump structure rather points to
the formation of dibaryon states with $I(J^P) = 0(1^+)$ and $0(1^-)$ near the
$N^*(1440)N$ threshold. This situation would be similar to the situation at the
$\Delta(1232)N$ threshold, where the signature of a number of dibaryonic
resonances has been found.
