Your statement seems to use Simple Probate and Affidavit of Death and Heirship as being interchangeable. They are not.
The proper probate procedures that will be required will depend on a number of things. Value of the estate, has a probate in a foreign state already been completed, etc. Standard Probate, Ancillary Probate and Simplified/Summary Probate all come to mind. Each has different requirements and procedures.
You only have to complete a probate in one county in the State of Oklahoma to cover all of the properties owned in the state. You then file a certified copy of the Decree of Distribution in those counties in which property is located. The proprieties should be described correctly in the decree.
I do not feel an Affidavit of Death and Heirship is substitute for a probate. It is not a legal conveyance or order. It is only a document in which someone testifies to "their perception" of the "facts". If completed 100% correctly it could become "marketable title" in 10 years. "Marketable title" has not encumbrance and is clean of defects so a court will require the purchaser to complete the purchase contract. Read some more about potential issues with an AoDH.
Quite often a company will lease you with a AoDH and then hold the production proceeds in suspense until marketable title has been established. Usually by the Probate that should have occurred in the first place.
The county clerk should not provide any legal advice on what the document being filed should accomplish. I have heard them doing such personally and have also assisted several people which received incorrect advice. The should only be telling the person if that documents meets the requirements to be "filed" in their office, not the power or effect that instrument will have.
If you completed a Simple Probate for your late spouse, you do not need to file Affidavit of Death and Heirship to go along with it in each county. You need to file a copy of the final decree in the counties.
That said, advice found on the internet is often incorrect. My points may be just as incorrect in your case. Find the right professional to assist you to keep from creating more of a mess that what already exists.