We know they do. An orbit is a mathematical object, and elliptical orbits only exist in universes that have exactly two objects with mass in them. Add another object, even far away, and as far as we know[0] we no longer even have a closed-form description of resulting motion patterns.
And our universe has tons of matter with gravitational mass everywhere, few other types of interaction beyond gravity, and a vacuum that just doesn't want to stay empty.
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[0] - Not sure if this was mathematically proven, or merely remains not disproven.
When I said "don't" I was talking about the complex shape that applies to orbiting the Earth, old school epicycles.
Actual orbits being slightly off ellipses isn't what I meant.