Everest isn't the point closest to outer space.
Earth is not a sphere: its radius is about 21 km larger at the equator than at the poles. Chimborazo in Ecuador is only 6,263 m tall but sits almost on the equator. Its summit is therefore roughly 2 km farther from Earth's centre than Everest's. Measured from sea level, Everest remains number one.
Useful: "Highest mountain" depends on your reference: sea level, Earth's centre, or the mountain's base.
Source: en.wikipedia.org