The same thing happend to me with a Edirol FA-66.
But the problem was not the guitar pickup that catch some shit from the monitor, beacause if I record at zero volume I can hear the feedback in mi DI track.
The problem seems to be a sort of feedback caused by the mix between audio output and direct monitor volume.
I have resolved the problem using the 3 and 4 audio output with the mix pot to audio output only and the volume audio output to zero, that control only the volume of 1 and 2 output, 3 and 4 output it's not affect by this control, and voilà there is not audio feedback in my track.