I notice that in playing the beginning of Bach's Toccata and Fugue in D Minor, some organists make an abrupt marcato release of the keys, clipping the notes, but others play the notes in a normal full legato. Is this just a matter of interpretation?
The three most important things in good organ playing are articulation, articulation, and articulation. It's almost the only tool that you have to define rhythm, accent, and phrasing.
Of course well-known pieces like BWV565 accumulate "performance traditions" the same way that ships accumulate barnacles, so let's look at what Bach actually wrote: http://imslp.org/wiki/Special:ImagefromIndex/01335
In addition to the (rather sparse!) performance directions in the score, it is apparent that this doesn't look like typical "organ music". It is thought that the piece was originally written (not by Bach, and possibly by Vivaldi) for solo violin, and later arranged (maybe by Bach, or maybe by someone else) for organ. So the first question for the performer is "do I want to make this sound like a piece for organ or for violin?"
The first 3 bars are in free rhythm. They don't establish any regular "beat", and the notation in bar 2 obviously does not add up to "one bar of common time". At bar 4-10 a regular rhythm starts to emerge, interrupted by a couple of pauses, ending with another cadence in free rhythm at the end of the first page.
So I think the issue is "what does the performer want to convey to the listener about the rhythm at bar 4?" If you play the notes legato, the listener will "hear" triplets starting on the first note, C#, not an anacrusis followed by triplets starting on D. And secondly, do you want to bring out the fact that if you play the Prestissimo section "in tempo" there is a repeated pattern three triplets followed by a duplet, or do you want it to be heard more as a rapid run in free rhythm? And do you interpret the notation literally, and continue "in tempo" right up to the rests, and then prolong the rests, or do you want to slow down at the end of each run and prolong the final note (A) as well as the rest?
Bach didn't indicate which option(s) he intended. A thinking organist will play the notes with an articulation based on his or her deliberate choice. An unthinking organist might just copy what he/she remembers (or misremembers) from the hundreds of times he/she has heard the piece before.
One look at the IMSLP score and you realize that this is not 'what Bach actually wrote,' though it is known he frequently played this. That particular score is not in Baroque notation, and even less in the style of Bach's well documented notational style.
Baroque notation was very spare, and would not have written out ornamentation, glissandi, and in particular, the huge arpeggiated chord at the beginning; rather, Baroque performance had an extemporaneous element, and such decisions were left to the performer.
If we are lucky, what we have is a transcription of how Bach actually performed it (it is almost certainly a transcription of how somebody played it).
The suggestion this piece was a violin partita is convincing, and there are a couple youtubes of reverse-engineered performances of excellent caliber. It has been proposed that the Bach partitas were actually compositions of his wife, Anna Magdalena. The plagal cadence ending the piece throws considerable shade on the idea that the original composition was by Johann Sebastien himself.