[Python] a mutable type inside an immutable container

I'm a bit confused about modifying tuple members. The following doesn't work:

>>> thing = (['a'],)
>>> thing[0] = ['b']
TypeError: 'tuple' object does not support item assignment
>>> thing
(['a'],)


But this does work:

>>> thing[0][0] = 'b'
>>> thing
(['b'],)


Also works:

>>> thing[0].append('c')
>>> thing
(['b', 'c'],)


Doesn't work, and works (huh?!):

>>> thing[0] += 'd'
TypeError: 'tuple' object does not support item assignment
>>> thing
(['b', 'c', 'd'],)


Seemingly equivalent to previous, but works:

>>> e = thing[0]
>>> e += 'e'
>>> thing
(['b', 'c', 'd', 'e'],)


So what exactly are the rules of the game, when you can and can't modify something inside a tuple? It seems to be more like prohibition of using the assignment operator for tuple members, but the last two cases are confusing me.

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