I've used $1 OVC on most my plane purchases. For a sale, I leave it to the buyer. I do report the sale to the FAA as required.
Oklahoma and Tennessee both will send you a letter saying you owe them money based simply on FAA transfer records. When I moved my J-3 project, which I inherited from my dad, from Missouri to Tennessee, TN tried assessing me an excise tax of 7%. When I was able to show it was 1) incomplete and not airworthy (no engine/prop) and 2) proved that it has been in the family since 1969, they waived it. On my Starduster Too, they sent me a letter stating I owed them taxes and that if I didn't provide a document showing purchase price (rather than my word), they would a price. I waited on them and paid the bill when it came.
My Swift, purchased in and registered in Oklahoma was taxed by OK at 3.25%. When I moved to Tennessee, TN picked up the change of address on FAA records and assessed an excise tax of 7%, minus the 3.25% I paid in Oklahoma...simply for moving.
My RV-4 took over 2 years before I got the letter from TN wanting their cut. While the BOS reflected $1-OVC, I had kept copies of check and memo info showing the price and what was purchased. They accepted that...and took their 7%. They waived fees/penalties for not reporting at time of sale, which most don't do on private sales.
While the state will get airplanes based on FAA registration transfers, including simple change of address between states, the DMV gets you when you buy car tags. My BOS for my CJ-7 didn't have an amount listed. The clerk simply asked me the amount and I told her the truth...and wrote a check for several hundred in taxes.
The taxman cometh regardless what is on the BOS. Government will spend thousands on manpower to collect $10.