  Till now almost 50 different data collections on the proton and neutron
electromagnetic form factors, also on their ratios, exist. On the other hand,
recently new very precise data on $\sigma_{tot}(e^+e^- \to p \bar p)$ from
threshold up to cca 13.5 GeV$^2$ have been obtained by BESIII Collaboration
using the initial state radiation technique with an undetected photon at the
BEPcII collider. In this paper a consistency of the $\sigma_{tot}(e^+e^- \to p
\bar p)$ data with the proton form factors behaviors is investigated, first
when the latter are obtained in the analysis of the proton and neutron form
factors data together by the advanced nucleon electromagnetic structure Unitary
and Analytic model, and then, as the neutron data are considered to be not very
precise, obtained in the analysis of only the proton form factors data in
spacelike and timelike regions by the advanced proton electromagnetic structure
Unitary and Analytic model. In both cases one finds the new
$\sigma_{tot}(e^+e^- \to p \bar p)$ data to be inconsistent with the curves of
$\sigma_{tot}(e^+e^- \to p \bar p)$ calculated by the proton electric and
magnetic form factors behaviors found in both analyses.
