I've been hoping for years that the advice about "no weeds in compost" was unnecessary. Weeds are almost the only green I have lots of. I was hoping that most weed seeds would rot or sprout and then die while in the heap, since I do turn it and it is always moist.
However, for two years now, I've had huge, dense monocrops of weeds spring up where I top-dressed with my compost.
I think it was good advice that I should have followed!