Why do the protons in pentacarbonylmethylmanganese show up at –0.21 ppm?
Unfortunately, you don't give an indication of what you expect the chemical shift for the -Me to be, other than higher than is observed. However, you are correct in your assumption; the &pi; back donation from the Mn centre to CO ligands does decrease the shielding, and therefore does increase the chemical shift, but this is a good case of how chemical shifts are all relative.

The dominating factor in shielding in d-orbital transition metal complexes comes from the paramagnetic ring currents within the incomplete valence d-shell. The circulating electron in the d-orbital produces a much greater angular momentum than for a p-orbital complexes (typically organic molecules, say). The influence of the d-orbital ring current induces a very large diatropic shift for ligands close to the metal centre. These can by very large for hydrides; up to -50ppm in some cases, and still significant for methyl ligands. 

So, your starting point for the chemical shift of the -Me ligand is something that has significant shielding, and would be largely negative. What you would expect, based on your argument, and indeed what is observed by experiment, is that as you increase the number of &pi; accepting ligands around the metal centre, you get an increase in the chemical shift of your -Me ligand. For example, as you go from M(PR3)5(CO)1 to M(PR3)1(CO)5, there would be a general trend to deshielding and an increase in the observed chemical shift.

Relative changes in chemical shift in transition metal/ligand chemistry are a great tool for determining stereochemistry and relative positioning of other ligands; a trans substitution will have a greater influence on the shielding than cis, for instance, however the overall dominating factor in the local shielding of your observed -Me still remains the diatropic shift from the metal centre.