I think it's most logical that unity change in some way. Especially as this icon is of a kind that is not that odd. If this problem effects all one colour icons this is a problem that should be tried to fix.
One possible solution would be to instead of using the average colour of the icon using a complement colour to the average colour. Don't know if this will look good but could be worth a shot. There is a few other ways to find colours that "fit" together maybe testing a few of them and see if any of them works better?
I think it's most logical that unity change in some way. Especially as this icon is of a kind that is not that odd. If this problem effects all one colour icons this is a problem that should be tried to fix.
One possible solution would be to instead of using the average colour of the icon using a complement colour to the average colour. Don't know if this will look good but could be worth a shot. There is a few other ways to find colours that "fit" together maybe testing a few of them and see if any of them works better?