While looking over some code in Think Complexity, I noticed their Graph class assigning values to itself.  I've copied a few important lines from that class and written an example class, ObjectChild, that fails at this behavior.
class Graph(dict):
    def __init__(self, vs=[], es=[]):
        for v in vs:
            self.add_vertex(v)
        for e in es:
            self.add_edge(e)
    def add_edge(self, e):
        v, w = e
        self[v][w] = e
        self[w][v] = e
    def add_vertex(self, v):
        self[v] = {}
class ObjectChild(object):
    def __init__(self, name):
        self['name'] = name
I'm sure the different built in types all have their own way of using this, but I'm not sure whether this is something I should try to build into my classes.  Is it possible, and how?  Is this something I shouldn't bother with, relying instead on simple composition, e.g. self.l = [1, 2, 3]?  Should it be avoided outside built in types?
I ask because I was told "You should almost never inherit from the builtin python collections"; advice I'm hesitant to restrict myself to.
To clarify, I know that ObjectChild won't "work", and I could easily make it "work", but I'm curious about the inner workings of these built in types that makes their interface different from a child of object.