Matthew 16-18 - "Whenever you fast, do not put on a gloomy face as the hypocrites do, for they neglect their appearance so that they will be noticed by men when they are fasting. Truly I say to you, they have their reward in full. But you, when you fast, anoint your head and wash your face so that your fasting will not be noticed by men, but by your Father who is in secret; and your Father who sees what is done in secret will reward you."
That should be Matthew 6:16-18.
It also does not mean that you have not washed your face or "anointed your head" (something no one does these days unless they are a male model) that day either.
I would also point out that Jesus is a Jew and he fasted on Yom Kippur like every other observant Jew does. No Jew fasted in secret on Yom Kippur - it was a universal practice.
Similarly, among Christians, fasting on Ash Wednesday and Good Friday is a universal practice.
It is clear from the context of the Scripture passage that Jesus was talking about the Pharisaic practice of not just fasting on Yom Kippur - like everyone else - but fasting twice a week every week and making a big show of it.
Here's another Chesterton tagline you might want to consider:
“The person who will not have a softening of the heart will eventually have a softening of the brain!”
Ashes are a sign of repentence. They are not a sign of fasting. Logically there would be no point to getting the ashes as a reminder of repentence if someone immediately washes it off.