Sorry for the sensationalist headline. Of course, the Ohr Hachaim (hakodosh!) doesn't really deny divine providence. Just he has an understanding of it that doesn't coincide with the official position we all were taught in Yeshiva. Here are the differences:
Official Position: EVERYTHING THAT HAPPENS TO YOU IS MINUTELY AND DIRECTLY CONTROLLED BY GOD. Not even a leaf can fall without God's express permission. If something terrible befalls you, its because God wanted it that way.
Ohr Hachaim: People have free will, and someone can exercise his (or her!) free will in a way that undermines God's plan
The Ohr Hachaim sees evidence he is right in the behavior of the Jacob's 12 sons over the last two parshas.
In Vayeshev, Reuven acts to save Yosef from the wrath after his brother's say, "Then we'll see what happens to his dreams.” According to the Ohr Hachaim, Ruven offers the following argument: "If you want to see if his dreams are true, you can't kill him, because no matter what God intends for Joseph, we can over-ride that divinely-intended destiny by exercising our own free will. Instead, let's throw him in the pit. Its full of animals, and animals have no free will. If the animals eat him, we'll know his dreams were nonsense, but if he survives we'll know God has something great in mind for him."
In Miketz, the brothers are imprisoned by Joseph for three days; afterwards, they are released and Joseph offers them a deal. Leave Shimon here as a my hostage, and the rest of you can go home. At that point, the brothers investigate their deeds and conclude that they are being punished for how they treated Joseph. Asks the Ohr Hachim, why are they performing this self-investigation now? Shouldn't they have looked into their deeds during the three days of imprisonment, when it was far from clear that they would ever be released? Why wait until now, when Joseph is delivering what appears to be good news and the ordeal, largely, appears to be over, to start searching for the cause of their misfortune?
The answer: The brothers didn't think their imprisonment was a function of God's will. They thought they were the victim of a free agent acting through his own free will. Only when they were released, and Shimon was separated from them did they start to notice parallels between their current situation, and the way the treated Yosef. Once again, a brother was being taken away, and that brother was the very one who had initiated the plot against Josef. The review of their deeds wasn't prompted by misfortune, but by the eerie parallels.