He began to keep a journal and was 'faithful to' it for years. [=he continued to write in his journal for many years]
The movie is 'faithful to' the book. [=the story told in the movie closely matches the story told in the book]
He was not 'faithful to' his word. [=he did not do what he said he would]
(..) Almighty God, bless the insignia of Saint Sebastian the Martyr, that it may contribute to the sacredness of him to whom it is given. Do you, Michael, promise to be faithful to the noble purposes of this Order, to have a special care for the poor, the needy and those who are ill? I do so promise. (..)1990 The Godfather Part III