Negative gravity is a confusing term because the problem wasn’t one of gravity, or even force, but rather of acceleration and inertia.
Negative gravity sounds confusing because the author is using the wrong word–what’s being described here is negative gravity equivalent (g-force). The aircraft is experiencing plenty of gravity, just in a different direction than it normally would. The problem is very much one of force.
Negative gravity is related to the concept of negative mass, which is a proposed form of exotic matter.