This is an interesting discussion.
I agree, partly, that Bach wrote music which can be interpreted as
jazzy. However, it's in my opinion the other way around. In jazz we use
sometimes phrasings which are equal to what Bach did and I agree: listen
to Bud Powell but also Brad Meldow (to mention a current pianist).
However, the harmonic complexity we use nowadays was not invented then.
Bach's music is primarily polyphonic (listen e.g. to the Brandenburger
concerts or the Goldberg variations) using, sparingly, simple chords.
One of the most "jazzy" elements in Bach's music is the "Basso continuo"
(often written with figures) and the greatest difference with jazz
bass-lines is the absence of rhythmic content.
In de realm of the classical music we have Debussy to thank for modern
harmonies together with the extensive use of the 6-tone scale and other
modern musical ideas. However the use of -9, -13 and many other
combinations in chords are 20th century ideas invented by jazz-pianists,
arrangers and "classical composers" alike and one of the latter is
Skriabin Take a look at his scores!).
The greatest difference between classical music and jazz, however, is in
my opinion simply the timing which is unbreakably related to jazz
melodies and harmonies. Try playing Bach with swing (the most horrible
example which springs to mind is Jacque Louisier) or Chopin or even Debussy.