In the mechanism you are considering, there are two options for reduction of R-$\ce{N^{.}H}$ (and similar for other neutral radical species)
$\ce{CH3OH + R-N^{.}H -> RNH2 + C^{.}H_2OH }$
$\ce{CH3OH + R-N^{.}H -> RNH2 + CH3O^{.}} $
In the first option (1) nitrogen oxidizes carbon - rare, but possible, as carbon has lower electronegativity. In option (2) nitrogen oxidizes oxygen - an element that has higher electronegativity, and this is unlikely.
In addition, in option (1) free radical is stabilized by forming 3-electron 2-center bond $\pi$-bond C...O, while in option (2) such stabilization cannot occur.
Taking proton (i.e. hydrogen cation) from $\ce{OH}$ is not an option for reduction, and $\ce{R-N^{.}H}$ is a radical, and expects hydrogen atom, not ion. Taking proton will produce $\ce{R-N^{+.}H2}$ and $\ce{CH3O-}$ and the first particle is not much better than the original $\ce{R-N^{.}H}$ while heterolitic bond breaking is generally less favorable, than radical one.
Proton may be accepted by negatively charged radical anions, like $\ce{R-N(O)O^{-.}}$ but after that they will seek a hydrogen atom for reduction.
Of course, it IS theoretically possible, that the radicals are actually reduced by tin and all the reaction happens on metal surface, and this is likely the case if the reaction happens in water, but in case it happens in organic solvent, especially reducing one like methanol, it is theoretically possible that it does participate in reduction. Until proper proofs, like trapping of the intermediate species, are obtained, any mechanism is no more then speculation anyway.