No, the 99% would not be symmetrical due to the definitions they are using. For the 99%, their definition of daylight includes all the way to astronomical twilight.
If you take a look at a city near the equator like Singapore, only 9 or so hours of the day are going to be "night" by that definition, and that will be the same in the winter as it is in the summer.
And if you take a look at a city like Seattle a little over half way from the equator to the pole, it is only getting a little over 2 hours of "night" at this time of year. In the winter it will still get around 12 hours of daylight when you include all the way through astronomical twilight.
So the numbers won't even be close. Maybe the 83% would be close to symmetrical for the sunrise to sunset definition of daylight. Although even there, isn't sunrise defined as when the first bit of the sun can be seen and sunset as the moment the last bit of it disappears? So there would be more daylight than night?
https://en.wikipedia.org/wiki/Sunrise#Measurement - sunrise is when the sun's center is 50 arcminutes below the horizon. 34 arcminutes of that is refraction, and another 16 is from the radius of the sun.
If the whole thing were symmetric, it would be 23.15 UTC on the day six months away (in early January). It's not quite symmetric because of the twilight issue.
