Consider two equal valued resistors connected in series. Connect one end
of the pair to +12 volts, connect the other end of the pair to -12
volts. *The voltage at the center is 0. There is certainly current
flowing. There clearly is power dissipated in the circuit.

you need to go back to circuits 101 and retake the undergraduate lab
intro where they teach you about measuring current and voltage. your
basic problem statement above is malformed since you can not measure
the voltage 'at the center'. voltages always have to be taken between
two points.

now if you REALLY want to be confused, ignore circuits 101 and draw
any circuit with as many components in it as you want as long as there
is only ONE loop. so connect AC or DC sources, inductors, capacitors,
resistors, around in a circle. start measuring voltage across each
one as you go around the circle and add them up. the result will
ALWAYS be zero. (go read about Kirchhoff's laws, here is one
reference http://www.bowest.com.au/library/theorems.html).

Note that of course these do not apply to transmission line problems
or antennas.