the cathode of the split load is indeed "following" the grid, but not
as much as a true cathode follower would. the reason is that there's
half the load in the plate circuit, and this is reflected back into the
cathode circuit as something like rp+rl/mu+1.
 
unless you're drawing grid current in either the concertina or the
output stages, the concertina will remain absolutely balanced (within
the tolerance of the resistor balance, as always). the impedance of
the cathode vs. the anode has nothing to do with this unless the
loads are not equal.
 
let's consider the ramifications of that fact... the current through
(and therefore voltage across) the plate resistor and the cathode
resistor is and must be exactly the same. 
 
the tube is varying its plate resistance like a small rheostat, back
and forth, thereby drawing the voltage divider (rk/tube's rp/rl)
together then letting it spread again. as long as rk=rl, in each instant
the voltage across the tube will be exactly CENTERED around the
b+/2 point... as much as vp goes down, vk goes up. the voltage
across each resistor is exactly the same at all times.
 
and get this--as long as the two resistors vary in resistance
together, the tube MUST remain centered around b+/2, since the
currents through each must be the same.
 
in other words, we're saying that the two load resistors for the
concertina are changing in resistance--but they're doing it at exactly
the same times. they remain balanced, and therefore the splitting
action must remain perfect. whatever distortion is coming from the
concertina with two CC resistors it's not coming from an imperfect
splitting of the phase.[1]
 
we're also saying that if you want to maximize imperfect phase
splitting distortion you use ONE carbon comp resistor, in EITHER
position, since it's change in resistance wrt voltage will NOT be
mirrored by its brother. 
 
kg
 
[1] there may even be a kind of reinforcement mechanism here,
with two CC on a concertina... accentuating the natural inability of
the tube to draw its cathode and anode together perfectly. as it
tries, the resistance of both rk and rl will decrease, since they both
have more voltage across them. this only serves to increase current
through the tube, which is already feeling the effects of saturation.
the "on" swing for the concertina will therefore be lower in
amplitude than the "off" swing, which will be reproduced in the
output as even harmonics... still, it's splitting phase perfectly.