I have a Fender Deluxe Active Jazz Bass thats makes this really really loud buzzing earthy sound. It seems to happen spontaneously, in fits and starts, but particularly if the cable input on the bass is moved, even the slightest bit. My cables, amp and pedals have been checked independently and they are fine. I've replaced the battery and had a qualified friend check the input and inside of the bass.

This sounds like either a bad guitar cable or a bad jack in the guitar. Possibly your friend is not as qualified to find these intermittent problems as needed? These jacks are really junky and often have riveting of the barrel come undone... especially if the retaining nut is overtightened. The LONG barrel like jacks are notorious for failing. You have all the information you need to solve this problem. First try a different guitar cable... (often they are broken or intermittent at the end where they flex). If that doesn't fix it, replace the jack in the guitar. Also verify that the conductive coating paint within the guitar is grounded. Sometimes the contact to it is destroyed when the volume control shafts or jacks become loose and they depend upon the shaft barrel to ground the paint.