However... If the burst phase is wrong, then there is no cancellation of
errors, because there are no "errors" /in the signal itself/. (Right?
(???))
Therefore, I don't see how line averaging can be used to eliminate the
need
for a manual hue control.

Think of the chroma signal as a vector with its y coordinate equal the
red difference component, and the x coordinate equal to the blue
difference component. A phase error rotates that vector about the z
axis. Effectively, the blue difference component receives a bit of the
red difference component, and vice versa.

On alternate lines the phase of the red difference component *only* is
inverted. In our view, this has the effect of reflecting the vector in
the x axis - what was a positive y value becomes negative.

The same phase error causes this vector to rotate in the same direction
about the z axis, but because of the reflection, the mixing of the
components has the opposite sign.

If you then negate the resulting red difference component of the second
line, and average with the red difference component of the first line,
the parts received from the blue difference component cancel out,
leaving a red different component that equals the original, multiplied
by the cosine of the phase error. The same applies to the blue
component. The result is that the hues are correct, but not as saturated
as they shoud have been.

No argument. That's always been my understanding. But...

If the burst phase gets screwed up somewhere along the line, no amount of
line averaging will fix the problem, because there's nothing "wrong" with
the subcarrier to fix.

Granted, this problem hardly ever happens. But the argument that a fully
implemented PAL set is inherently immune to color errors is hard for me to
swallow.