The question Did a spacecraft ever use an atmosphere to accelerate away from a planet? was unfortunately given five down votes and answered with:
Entering the atmosphere introduces drag, which could only reduce your energy.
Your premise is incorrect. In no case does "skipping off the atmosphere" leave you going faster than you arrived, engines on or not.
and yet a few days later the New York Times said of a 2017 fireball (quotes are from "Patrick Shober, a graduate student at Curtin University in Western Australia who led a team that studied the event" which was measured by the Desert Fireball Network published in arXiv as Where Did They Come From, Where Did They Go. Grazing Fireballs and will be published by The Astronomical Journal):
By triangulating its trajectory from multiple positions, Mr. Shober traced the fireball back to the asteroid belt between Mars and Jupiter, his team reports in a paper that will be published by The Astronomical Journal. As it reached Earth, the planet gave it an extra kick.
“It gained orbital energy from the close encounter the same way a space mission might use a slingshot maneuver,” he said, referring to the orbital navigations NASA and other space agencies use to speed robotic probes toward their destinations.
That sent it careening toward Jupiter, giving it an elongated, outbound orbit more like a comet’s than an asteroid’s. Its path interests astronomers, who can’t study anything this small through a telescope.
Question: Superficially at least it seems the quotes in the NYTimes seem to contradict those answers, but do they? Or do they perhaps just need some refinement (e.g. gain/lose energy with respect to what or in which frame)?
Further reading from the arXiv preprint.
4.2 Short-term Simulations
… As a result of the grazing encounter with the Earth, the meteoroid was flung into an orbit with a higher energy (Fig. 8). The geometry of the encounter enabled the meteoroid to gain angular momentum around the Sun (Fig. 10). As a result, the semi-major axis and eccentricity both increased due to the increase in energy, and the object was inserted into a JFC (Jupiter family comets) orbit. Hereon, the object’s future is strongly governed by its interactions with the gas-giant. Fig. 9 shows the evolution of the orbital elements for the meteoroid ±100 years relative to the grazing encounter.