Not to put too fine a point on this, Corky, but you can in fact enter a
climb and still maintain 1 G downward relative to the axis of the
airplane, but you have to decelerate while starting the climb. I agree
that you can't climb at a steady rate and not experience a shift in g
forces aft, but as your bring the nose up you have to slow down as
well, to add a little negative acceleration to offset the aft shifting
gravity vector. Think of it this way. If you hang a plumb bob in the
airplane, and start a climb, the bob will shift aft. If you're in level
flight and slow down, it'll shift forward. If you combine the two
correctly, it'll stay pointing at the same spot on the floor.

If you agree with this reasoning, you'll also agree that with a fast
enough entry speed you could pull through an entire loop -- it wouldn't
be round! -- and keep the plumb bob centered over the same spot.

Think about it, sitting at the keyboard typing, and flying along in
level flight, you are at 1G. Pull back on the yoke or stick and you
are no longer at 1G, you are at 1G plus whatever it takes to climb.
It's impossible to gain altitude without experiencing more than 1G.

Could it be that the person describing the 707 barrel roll meant that
the maneuver was 1G in excess of 1G? In other words 2G's? Could be,
but probably the announcer or "talent" speaking for the clip had no
idea what he was talking about.