The Mayflower "Silver Books" (Mayflower Families through Five Generations series) is at the time of publication a totally valid source. However, after their publication, future discoveries may be made which may invalidate some lines or add other lines of descent.
As was mentioned previously, your line through Abner Fuller and his father John Fuller is still valid.
I have recently co-authored an article (in The Mayflower Descendant) documenting where Capt./Dr. Matthew Fuller of Barnstable could not be a son of Edward Fuller of the Mayflower. The General Society of Mayflower Descendants (GSMD) currently is not accepting applications through this line. They are accepting lines of descent through Samuel Fuller (born 1608) as son of Edward Fuller.
The GSMD is in the process of creating a new Silver Book for Edward Fuller. As part of this process, they are conducting research in England to hopefully determine whether Capt./Dr. Matthew Fuller was a step-son of Edward Fuller (that is to say, Matthew may possibly be a son of Mrs. Edward Fuller by a prior husband, who also had the Fuller surname).
Once this new Silver Book is published, the GSMD will no longer accept the previous edition, but in all honesty, this doesn't really matter as the current GSMD application process does not require documentation for any information they have already published in the Silver Book series (as long as this information has not been contradicted by a more recent publication like the Mayflower Descendant article I co-authored).