Not quite true.
Nucleophilic attacks can either be favoured by a charge interaction (for a polarised substrate - eg. a carbonyl (+)C=O(-)) or an orbital interaction (for a not polarised subtarte - eg. your MeBr)
Charge-interaction type nucleophilic attack is favoured by a charged/ strongly polarised nucleophile; eg. OH-
Orbital-interaction type nucleophilic attack is favoured by a good orbital interaction. (good energy match, large orbitals, etc) eg. H2S:
Hydrogen sulfide is a better nucleophile in this particular case, because the C-Br bond is not polarised, so a good orbital interaction is needed for a good nucleophilic attack. Water is not as good a nucleophile because its lone pairs are more contracted in smaller orbitals which do not overlap well with the C-Br sigma* orbital in the SN2 reaction.
In other cases, depending on the subtrate, water may be a better Nu- than H2S.
Basicity do not relate well with nucleophilicity.
H-bonding of the nucleophile doesn't affect its nucleophilicity.
There are no 'theory' to say that water is a better nucleophile than hydorgen sulfide; but Water is a stronger base than H2S as a fact. (pKa H2O 16, H2S 7)
You need to think in terms of Orbital interactions (relates to polarizability), geometry of the subtrates, favourable charge interactions, effect of solvents etc.
for deciding on nucleophilicity of your nucleophile in an SN2 mechanism.