There's no telling when a teacher's influence will ever end (photo).
The thought of being able to study with a student of a student of a student, etc., all the way back to some famous composer or virtuoso organist from history is an idea, a nice one at that, which might help us better see the big picture about carrying on the tradition of organ playing as passed down through previous generations.
We need to be aware, of course, of the perils of placing a blind trust in genealogy, as different organists in an unbroken chain of generations of teacher-pupil succession have not always been consistent in observing or passing along everything they learned from their teacher(s).
In addition, teachers are subject to the revolutions in thinking of their own day which may impact very strongly on their ideas of the traditions they need to be passing along to their students.
In some cases this can be so powerful an influence that it can even change the definition of what constitutes a "tradition" in organ playing.
Therefore, having a traceable lineage back to some famous musician does not give us a bulletproof guarantee that everything we've learned from our teachers is identical in every respect to some "tradition."
What it DOES do, is that it creates a responsibility on each of us to be better, to practice more, to be the best we can, and to spread our message as far as we can.