no, that's silly. if both admitted the oral agreement, it wouldn't be in the courts. and that's why we have a discovery process in law, isn't it - like an email trail to prove the verbal agreement actually existed. it's cute to say an oral agreement is worth the paper it's (not) written on but that only shows a lack of understanding case law.
One of the most famous cases where a verbal contract was enforced in court is Pennzoil Co v. Texaco. In 1984, Pennzoil bought Getty Oil through an oral agreement, but later sold it to Texaco for a higher price. Pennzoil filed a lawsuit against Texaco, claiming they broke the oral agreement, and won. Pennzoil was awarded $9.1 billion in damages, plus interest and penalties, which was the largest award in US history at the time.