It is not within the statute of frauds. Therefore the fact that it is oral is not an issue.
Consideration is a bargained for exchange of something of value.
Burnham clearly got something of value, but Goodheart did not, for Burnham did not have a good claim. It would seem to be the better rule that if a party thinks the consideration has value, the contract is enforceable even if it turns out not to have value. As stated above, both parties apparently believed that Burnham had a good claim. This belief was not in accord with the facts. It is a material fact that goes to the essence of the contract.