I don't think the oil supply will really be a problem now that Iran's sanctions have been lifted. They will look to sell as much as possible to fix the damages their economy have suffered due to the sanctions and they'll flood the market. Other countries will do the same as well because their public finances are badly hit by the low oil prices.
Why is everybody all of a sudden believing what the Saudi's say all of a sudden? What they do and what they say has been two entirely differebt things in the past, so now it comes to oil I'm not sure they should be believed either.
Well, their economy is suffering quite a bit from the drop in oil prices and they're burning through their money reserves fast just to keep their current level of spending in order to keep potential unrest at bay from their local population. I think they don't really have much choice now. They have to increase production.
Saudi Arabia could have afforded to stop more oil production until prices rise some time back but this is no longer untenable. More countries are striking oil and are not into cartels. Regional geopolitics will also challenge their position. The fact that sanctions against Iran have been lifted is not good news for Saudi Arabia. They might even be forced to pump more oil into the market to throw a spanner into the works to get at Iranians who are a rival regional power.