That article is claiming that the accelerations some have computed based on instrument readings for some unidentified objects are impossibly high. To avoid this impossibility, they claim that the only logical explanation is that the craft are curving space time in such a way as to actually have 0 acceleration, which they claim is somehow possible.

First of all, the only theory of curved space-time that we have doesn't allow 'at will' curving, by simple conservation laws. Second of all, the amount of curvature needed to achieve the apparent acceleration is proportional to that acceleration, and so is the mass-energy required to produce that curvature. If it were possible to curve space time so much that you appear to accelerate at 12000g, you should also be able to accelerate to 12000g. I haven't done the math, but I would expect the amount of mass required to be well above the Schwartzschild limit, meaning that whatever the UAP was before attempting such a maneuver, it would quickly become an easily-identified black hole afterwards.

Obviously, the explanation that is far more in line with current physics than the article's exotic space-curvature drive would be various glitches in the instruments used to assess the speed of the 'objects'.

Looking up the math a little bit, and assuming that in order to curve space-time enough to achieve 12000g you would need a mass that is 12000 times the earth's mass, the Schwarzschild radius for such a mass is 106m.

So, if the observed object was less than 212m across, it could not have appeared to accelerate at 12000g by curving space-time without collapsing into a black hole.