This isn't correct in the case of object literal methods. This will also break if @sandersn's work goes in to contextually type subclass properties.

Can't you just check if you're in a parameter and you have a contextual type? Why do you need to bring the parent into this?

object literal properties are handled in the branch above.
The check if parent has contextual type is necessary to make sure that the type that we'll obtain from getTypeAtLocation is backed up by something (contextual type of the function) and not just implied by the shape of object binding pattern

discussed offline: need to support cases when completion is requested at position $

interface Foo { m(x: { a: number, b: number }): void }
let x: Foo = {
    m({ $ }) {
    }
};