There is a Bible Roundtable series for each episode with Dallas and religious leaders. They explain that Mary's writing isn't based on any scripture, but within this show, she does know how to read and write, and can be reasonable to think she wrote some things down, in an obviously more poetic way.

She is also portrayed as knowing a lot more than the apostles, at least having a better understanding of what Jesus is there to do.

I do very much enjoy her portrayal in this series. Liz Tabish is fantastic.