I in no way want to compete with Mark's answer, but just wanted to highlight the piece that finally made everything click as someone new to Javascript inheritance and its prototype chain.
Only property reads search the prototype chain, not writes. So when you set
myObject.prop = '123';
It doesn't look up the chain, but when you set
myObject.myThing.prop = '123';
there's a subtle read going on within that write operation that tries to look up myThing before writing to its prop. So that's why writing to object.properties from the child gets at the parent's objects.