Burnett was widely known to be an eccentric. Habitually he rode on horseback between Edinburgh and London instead of journeying by carriage. Another time after a decision went against him regarding the value of a horse, he refused to sit with the other judges and assumed a seat below the bench with the court clerks. When Burnett was visiting the Court of King's Bench in London in 1787, part of the floor of the courtroom started to collapse. People rushed out of the building but Burnett who, at the age of 71, was partially deaf and shortsighted, was the only one not to move. When he was later asked for a reason, he stated that he thought it was "an annual ceremony, with which, as an alien, he had nothing to do".