Ed_G wrote:

If both shields, ( ungrounded ) are tied together, and the two center conductors are acting as a 'balanced' feedline, how can current
flow on the outsides of the shields, if the interior currents of the two
center conductors are always 180 out of phase?

The answer is that making the feedline physically symmetrical doesn't
make it "act as a balanced feedline". A feedline is balanced and not
radiating only when the common mode current is zero, i.e., the currents
on the two conductors are equal in magnitude and opposite in phase.
Making a line physically symmetrical doesn't guarantee or cause this.
Nor, for that matter, does making a line physically asymmetrical (e.g.,
coax) necessarily cause a line to become unbalance. There's more about
this at http://eznec.com/Amateur/Articles/Baluns.pdf.

Roy Lewallen, W7EL