You are correct about the worth of the case. Your aggregate was for under $50, and that would mean you can only be charged with a misdemeanor. The statute of limitations for the misdemeanor is three years in Oklahoma. However, the statute ceases to run under certain circumstances. So, assuming you were not an Oklahoma resident or you were but you were absent from the state, the Statute of limitations would get an extension. I don't know if that applies at all, but you do and that may be what you're missing.
They can legally threaten you with an arrest, because they believe they have an argument that will overcome your statute of limitations objection. If you don't believe they can do it, you can call their bluff, let the warrant issue (or not) and hire a lawyer and make your statute of limitations argument. If you're right, the case will be dismissed and you can look into your civil remedies for false arrest
The "diversion fee" is a fine that keeps the case out of court
and the charges off of your record. The charges would never be filed but the matter would be "diverted" to allow you to take care of it through the DA. If you let the case get filed with the court, on the other hand, the arrest and ultimate conclusion of the case will appear on your RAP sheet.
As for your next move, a local lawyer may be able to straighten this out for you.