= Solution
The <Cosmic neutrino background> began free streaming at <neutrino decoupling>, long before <cosmological recombination>, so its directional flux can retain information about density fluctuations from epochs inaccessible to the <Cosmic microwave background>. Earlier decoupling does not by itself guarantee a larger <comoving radial distance>. A sufficiently massive neutrino eventually becomes nonrelativistic, and its travelled distance is
$$
\chi_\nu=\int_{a_{\rm dec}}^1\frac{v(a)}{a^2H(a)}\,da,
$$
which may be smaller than the photon distance because $v(a)<c$. Hence the <cosmic neutrino background last-scattering surface> need not lie beyond the <Cosmic microwave background last-scattering surface>; it generally does for neutrinos that remain sufficiently relativistic for sufficiently long.
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