  The high-statistical KLOE data on the $\phi\to\pi^0\pi^0\gamma$ decay are
described simultaneously with the data on $\pi\pi$ scattering and the
$\pi\pi\to K\bar K$ reaction. The description is carried out taking into
account the chiral shielding of the putative $\sigma (600)$ meson and it's
mixing with the well-established $f_0(980)$ meson. It is shown that the data
don't contradict the existence of the $\sigma (600)$ meson and yield evidence
in favor of the four-quark nature of the $\sigma (600)$ and $f_0(980)$ mesons.
