I know that sulfates can be reduced by H2
S to elemental sulfur, something like
S + 4H+
but it is not exactly sulfate reacting with itself. Hydrogen sulfide can be produced by a process (or rather family of processes) known as thermochemical sulfate reduction (TSR). TSR requires some reducing agent, for example hydrocarbons - hydrocarbons react with sulfates producing hydrogen sulfide, which in turn reduces sulfates to sulfur.
Doesn't look like it fits what your prof is suggesting. Could be there are other possible mechanisms, can't say I know much on the subject, I just happened to read not long ago about sources of hydrogen sulfide in crude oil and natural gas.