A participant had a stormy relationship with
his wife and were constantly separating. He died
and she has come forward to claim a QPSA. However,
some coworkers believe they may have been divorced
prior to his death. She says they were not.

How does an admin effectively research this issue?
There is no record of a divorce on the county records,
but they could have done it elsewhere.

While rules regarding the filing of a divorce may vary from state to state, I believe that divorces are generally filed in the County of residence of either the petitioner or the respondent. (It's been way too many years since I studied Domestic Relations.) If both parties lived in the same county, it is likely that the divorce would have to have been filed in that county. You might want to consult a local attorney to determine what your state rules are.