Even for manual trannies it isn't that easy.  There is a critical
throttle opening, somewhere around 3/4 that provides best economy, but
it is hard to find, and you must take the car out of gear and coast
down that way (or with clutch in).

Now, there are these special built cars where there is NO throttle and
the car is accelerated to a pre-computed speed, then coast down. But
on these cars the carburetion or injection systems are readjusted for
no power enrichening, or the engine never had that feature in the
first place.

I doubt if her technique really works in practice, in traffic on
normal roads. It can work on a test track IF the person doing the
tuning setup is sharp enough, but they have to know a lot about that
particular engine.

On the other hand, there is ONE truth to this.  A frequent admonishion
for good economy is to avoid "jackrabbit" starts.  But they neglect to
define what they mean by a jackrabbit start. It does NOT mean to start
off with very little throttle and creep slowly up to cruise speed.
That wastes gas. In stick shift cars best economy is obtained by
accelerating at about 60 to 70 percent throttle, and shifting very
early.

On automatics, that can hold shift points too high, so the value of
optimum throttle opening drops to maybe around 40% or so- depends on
the car.  In practice, what this means is accelerate normally.  There
are other ways to avoid high gas consumption like driving the speed
limit, avoid tailgating, and look ahead and play traffic lights.
Brakes are the biggest deterrents to gas mileage- avoid using them
except in an emergency.