I guess it means the pilot managed to provide a net 1 g of
acceleration upwards, so the body and any other object experienced the
usual head-to-toe force.
But to achieve that (1G) acceleration it should flew with 2 g of
acceleration (to compensate the gravity first). She said the flight
path was pretty straight.
No, you are mistaken here, unless I am misunderstanding your meaning, which is possible. (These concepts are kind of "squirrely" -- the net acceleration on the aircraft is indeed 2 G if the aircraft is inverted and the occupants are experiencing the same sensations that they'd feel in normal upright flight, but there's no "compensation" going on. Read on for more.)
The net acceleration in "usual" life is actually 0 G.
For example, standing on the ground, the ground is pushing up on our feet with a 1 G upward force, and gravity is pulling down on our body with a 1 G downward force.
Flying straight-and-level, the aircraft wings are generating a 1 G upward force, which is transferred through the aircraft structure, and ultimately through the seats, to our body, while gravity is pulling down on our body with a 1 G downward force.
In what we call "0 G" flight or "weightlessness", the aircraft wings are unloaded (i.e. the angle-of-attack is reduced) so that they generate 0 G of force. Gravity still pulls down on us with 1 G of downward force, so the net force is 1 G downward.
To experience the sensations of normal upright flight while inverted, the aircraft must generate 1 G of force in the "upwards" direction in the aircraft's own reference frame. This means the aircraft must generate 1 G of earthward force, i.e. toward the ground. Meanwhile, gravity is also pulling down with 1 G of earthward force. The net force is 2 G, acting in the earthward direction. So the lift force generated by the aircraft is not compensating for gravity, rather it is adding to the effect of gravity, in terms of the net acceleration experienced by the aircraft.
You can see why this would not be sustainable for long-- the flight path is going to be curving earthward very rapidly. Even if the segment starts with the aircraft's nose pointed well skyward, it will soon be pointed steeply downward.
However, it's been pointed out in a comment that even a slight mild positive G-loading generated by the aircraft will produce sensations that might be hard to distinguish from the normal full positive G-loading of 1 G, especially for an inexperienced passenger. Still, even if the aircraft was producing a positive G-loading that was just barely above zero, the net acceleration on the aircraft will still be slightly more than 1 G earthwards, so even in this case the maneuver is only sustainable for a relative brief interval. It's pretty clear that your informant is simply not reliable-- either she is not remembering her perceptions clearly, or she was too overwhelmed by the newness and strangeness of the experience to clearly perceive what was really going on. (Especially this part: "She said the flight path was pretty straight.")
"Reading between the lines" of this answer, I hope you can see that the only force we actually feel in flight is due to the real aerodynamic and thrust force generated by the aircraft. We don't "feel" the force or acceleration component that is due to the pull of gravity, because gravity acts "from within" and exerts an equal pull (per unit mass) on every particle of our body, creating no stresses or strains, and thus no sensations.
Disclaimer: this answer is written from a Newtonian perspective, treating gravity as an actual force.
Disclaimer: this answer has treated G-loading as a measure of force as well as acceleration. Strictly speaking, G-loading is not actually a measure of force, but a measure of force per unit mass, which is the same thing as acceleration.