Did you call the clerk first, or the depository first?
If the records are being kept at the depository, then you order copies directly from there at, Illinois State University (for Livingston County).
If the depository stated that they don't have the records for a particular county, and then the county claims they were destroyed by fire, then there is not much that can be done.
But I think I would call back the University and ask the IRAD volunteers where the records are for that county and year, and how you can obtain at least an "abstract" of the record for a few dollars copy fees.Did you need a certified copy as opposed to a regular one?Probably not, is my guess.
It makes no sense that there was a fire in 1890 or 1920, long before the process of recording these licenses began, which is in the 1990's.