I will try to explain what I think is going on here, from the information you have given. The way it is supposed to work for out of state purchases is: You pay for the car only and no sales tax or tag/title and you go to your state with the purchase paper work and pay tax/tag/title and any personal property tax your county may require. Some times as a courtesy, if the dealer has knowledge or prior transactions with certain states, they will do the paperwork and take sales tax and process the tag/title. This mostly happens in borderline states like here in NC and SC.
Another possibility is the dealer as a courtesy took sales tax as part of the overall purchase price and will transfer the sales tax to the state you live in. Then all you have to do is process the tag/title in that state. But in your case they took the incorrect amount equivalent to NC. I seriously doubt they gave it to NC since they absolutely knew you would register the car out of state.
So I am thinking OH will get the 3% sales tax from the dealer then you must pay the additional amount since you are responsible for the full sales tax amount. Yes the dealer made an error, but is not responsible for the sales tax. You are clearly the one that must pay the whole amount.