No, they do not. In fact, it is possible that a Seller would counter a full price offer with a number higher than the asking price. The Seller is not legally required to accept an offer just because it is full price.
I have never been part of a transaction where this happened — except in competitive situations where other buyers were competing against my buyers for the same (no doubt under-priced) home. In those cases, the final sales price could be upwards of 30% or more on top of the listed asking price.
Is under-pricing your home in hopes of a competing-offer frenzy a smart marketing strategy in the Columbus Ohio Real Estate Market? Not usually. The best way to price your home is still pricing it at the place where it is most likely to sell, depending on what the market will bear, for the most money in the least amount of time possible.
Possibly of interest: