You're taking it too literally. The 'nudge' means a change in initial conditions, and could result e.g. from measurement uncertainty, not necessarily a literal nudge.
It also doesn't necessarily matter that much if there are more than two bodies, if the gravitational influence of other bodies is small enough, then you can model as a two body problem.
It also doesn't necessarily matter that much if there are more than two bodies, if the gravitational influence of other bodies is small enough, then you can model as a two body problem.