Can you tell us exactly how you're arriving at this number?
Are you by any chance measuring the percentage of the area on that map that is illuminated vs dark?
Because if you're doing that, you need to be careful which of the four progressively darker contours you're measuring against.
The first one, i.e. the brightest part of the map, is the only one showing where the Sun is visible above the horizon. This is the one that is 50%* of the total area of the map, as one would expect on an illuminated sphere without an atmosphere.
The other three show various grades of twilight - this is where the Sun is below the horizon, so it doesn't shine directly onto any part of the Earth within those contours, but its light reaches the surface through a combination of diffraction and scattering in the atmosphere. In this way a sphere covered in an atmosphere-like medium can be illuminated more than 50% at any time (this is not specific to the 8th of July, but any day of the year). If you're measuring against those, you'll get more than 50%. But, again, in this case it is not direct sunlight.
*I'm not sure the map goes into that much detail, but even the first contour should cover a little over 50%, as the aforementioned diffraction (bending of light) makes the rising/setting Sun briefly visible above the horizon even though it is geometrically below it.
