Oh god. If only you knew the can of worms you were stumbling into!
This comes up pretty frequently. Luke, bless his anger-filled little heart, is trying to reflect medieval reality here. Most people did not learn to read and write the same way we do these days. In fact, it was pretty much only clerks (studying to become priests) that learned to read (and not all of them). They did not receive a piece of paper and a pen and learn how to make the letters to piece together into words.
Instead, they looked at a Bible with an instructor and learned painfully and laboriously what particular words looked like. They simply did not learn how to write as they learned how to read. In fact, it is only after the Enlightenment that people started learning how to read silently! Before that, because of the way they learned, they were incapable of not mouthing the words as they read.
Writing was an altogether different kettle of fish, and only for the truly educated. You would not be able to write a letter without knowing how to read.
HOWEVER. It is possible to write words without understanding what is being written. In fact, it was fairly common (at least among monks) because, except in rare cases, the only thing that was being 'written' was the Bible. They simply sat down with a Bible and copied the symbols they saw without understanding them.
If a player takes Writing and does not take Reading, the skill should rightly be Copying.
I corner him and stab him in the face!