My understanding is that the single-celled organism
Clostridium botulinum that causes botulism poisoning is itself harmless. It is the toxic chemical this bug produces that is dangerous (have seen it described as "the most lethal toxin known to man"). The toxin is a waste product that is produced by
Clostridium botulinum during its normal functioning in oxygen-deprived (anaerobic) environments - much like a yeast cell happily produces CO2 and alcohol as waste product in the normal coursse of its life.
According to a referenced article in Wikipedia,
Clostridium botulinum is commonly found about the home. If ingested by a non-infant the acidic conditions of the gut prevent the bug from functioning - so no toxins are produced. However, kids under 1 year old have not yet developed their full digestive juices so they can die if they ingest the bug).
The botulism toxin is destroyed above 60 degrees C, but the spores of
Clostridium botulinum can survive boiling, and if they do and they later arive in conditions (such as temp. pH, etc.) that are favorable, they can start growing and reproducing and in doing so will produce more of the toxin as a waste product.
I thought this picture might help show where in the brewing proccess the likilhood of botulism contamination would occur in the No Chill method (if it is likely at all). Remember the wort might be free of
Clostridium botulinum and its spores coming out of the wort boil, but if spores exists in a dirty cube container they might survive (?) to grow and reproduce as the wort slowly cools to morre ideal temperatures).
(Pic sourced from G. Menz. P. Aldred, & F. Vrieskroop, 'Pathogens in Beer', in V.R. Preedy (ed.),
Beer in Health and Disease Prevention, Academic Press (London, 2009), p.407 - the coloured graphical additions are mine. Book is available by online by searching Google Books).