Well hang on, maybe we're thinking in terms of stable orbits.
Stable orbits are eliptical. But unstable orbits could be as you describe, without relying on the topography to explain the 2 minima/maxima.
Rough example - stand on the moon (massless; thought experiment), shoot a cannon just to the left of the earth - it goes way past the earth then returns just to the right of the earth, keeps going in an obloid, unstable orbit for some time.
I may be explaining poorly, but TL;DR - unstable orbits don't have to be elliptical?
Not my best area of expertise, but I think that's close to right