I should qualify this statement by saying that technically, it's probably true even though there is no practical way to prove or disprove. I also understand that it's not intent is not to suggest that that given the right circumstance, that this could be done.
My philosophy is that even if an infinite number of monkeys could reproduce the works, the resulting stories would be a result of nothing more than random, persistent, and likely - very annoying - hammering on the keyboard without having any concept of what a story is. In this world, the words and the story are not the result of someone crafting thoughts, plots and characters and to me, this makes all of the difference.
The spirit, the passion, the commitment and the creative, this is what for me really makes a story. The question has never been asked, could an infinite number of monkeys create a story - one that entices, entertains and enthralls. This is what defines a writer.