The heap invariant is also required in order to even meet the documented behavior of returning the smallest item.

>>> import heapq
>>> li = [5, 7, 9, 1, 4, 3]
>>> heapq.heapify(li)
>>> li
[1, 4, 3, 7, 5, 9]
>>> li[2] = 0
>>> heapq.heappop(li)
1
>>> li
[0, 4, 9, 7, 5]
>>>

I guess the argument could be made that docs say "from the heap", and by modifying the list yourself it's no longer a heap.