I got this wrong both times, but for anyone who needs a simplified explanation here is my understanding:

E is correct because it is getting at the author's assumption by taking for granted that 'not straying too far from the melody' is the end all be all, and fails to consider other important elements that could classify the later music as Jazz.

A wrong because the first half of the AC could fail, and the music could still feature amount of improv. The argument could still work out and thus not weaken. If this AC was written the author way around, then it could work. However, this goes back to the conditional relationship fundamentals (i.e. SC can fail, NC can still happen or not. If NC fails, the SC fails automatically).

Be careful of choosing ACs with SC/NC indicators.