The surface of the Earth is the only place we know of where a natural satellite appears exactly the same size as the primary / only star.
Perhaps it's the only place we know of on a planet's rocky surface. But most of our solar system's planets with moons don't have rocky surfaces, and we can't detect moons in other systems, so you really mean it's not true from the surface of Mars, Pluto or Charon.
Additionally, the moon varies in apparent diameter by about 13% from apogee to perigee, and the sun by about 3%. So while it might appear "exactly" the same size at some point in its orbit, mostly it's just within 5%.
Edit: only by a few percents; the distances are too large to appreciably change the visible size of the sun in the sky.
David Kipping's Cool Worlds lab at Columbia has done some promising research on this, some of which is detailed in excellent videos on their youtube channel.