It's not clear whether the TW2010 loading coil box, or "middle section" contains a balun or not.
Unless it's hidden on the back side of the board, there seems to be no balun in the photo of the loading coil box on p. 26 of the following PDF: http://www.twantennas.com/pdf/24-TWReviewWestSept.pdf
One item of note in the above PDF is that the control cable
(to control the coil switching) is apparently 65 feet long. That might have something to do with the recommendation of a 65-foot long coaxial cable feedline, though I can't imagine exactly what; perhaps the coax and the control cable can interact in undesired ways.