I can't see anything different in the 2 schemes around the feedback. Both lack the cap in series with the control that I'd added, but then Mr May's examples probably lacked it too. The cap would have changed things a bit, since it would have cut some of the bass in the feedback, and in the Foxx, both the phase shifted AND clean signal get fed back.
The feedback is positive, which, where the clean signal is involved, usually leads to uncontrolled howling, so you get quite a small range of adjustment between a useful feedback amount and rampant squeel. The cap I added probably gave a bit more useful range.
The original reason for adding that cap, was to isolate the first amp from any ground or DC voltage sneaking in from the output and changing the bias of the first amp. Normally, you would hope whatever it's plugged into would have a cap on it's input to stop this ever happening anyway. In the real world, you can't guarantee this is always the case, so I would add a cap in there anyway.