As fake as the letter probably is, it couldn't be from a someone hoping to become the prince's fiancee. The whole 'fake fiancee' bit would be so tightly under wraps, that very few people would know about it.
The problem is, who would want the MC to be 'fired' from her role? The prince's aid might want the prince to get a new fiancee, but he doesn't seem like the type to dismiss her via a sudden, late night letter.