We do indeed have an exothermic reaction between hydrogen sulfide and silver, which goes against the usual EMF series. The EMF series applies specifically to species in water solution, so we should not be surprised that it does not hold when we go to gas-phase reactions (even with steam, let alone with hydrogen sulfide).
We compare the standard enthalpy changes associated with oxidation of silver by water vapor and by hydrogen sulfide (technically, we should be using free energies but the enthalpies make the point and are easier to come by). Using the data from this table:
$\ce{2Ag + H2O -> Ag2O + H2}; \Delta H =+210.7\text{ kJ/mol}$
$\ce{2Ag + H2S -> Ag2S + H2}; \Delta H =-11.2\text{ kJ/mol}$
The reaction with water comes nowhere near being thermodynamically favorable, whereas the reaction with hydrogen sulfide releases energy and thus may be favored.
This selective reaction of silver with hydrogen sulfide may be explained in tetms of molecular-orbital structure. Sulfur atoms are large with valence orbitals having multiple nodes, which leads to poor covalent overlap and thus weak bonding with hydrogen. Therefore some metals that cannot break the hydrogen-oxygen bonds of water, or do so only with difficulty, may break the hydrogen-sulfur bonds of hydrogen sulfide. Silver is one of several late transition and post-transition metals with this selectivity; these are the chalcophile metals that often occur in nature as sulfides.