It just depends how you measure "closest".
Similarly, Mount Everest is the highest mountain (above MSL), however Mauna Kea is higher if measured by prominance (starting from its base which is under water).
Similarly, Mount Everest is the highest mountain (above MSL), however Mauna Kea is higher if measured by prominance (starting from its base which is under water).
Of course in reality neither are the highest mountain, that honour goes to Chimborazo, a good 2.1km higher than Everest (when measured from the Earth's centre)
According to CGP Grey's video linked in the comments, not only Mercury has lowest average distance to Earth, it's also spend the most time being the closest planet to Earth, so it already met two definitions I can think of.