While I agree with you that this is most likely nothing more than a lie from Ali al-Naimi, there's one other possibility that I find intriguing:

The Saudi's have known about additional oil deposits for years or even decades, but they've never considered them reserves because of the very high cost of extraction.  As HO suggests, the combination of higher market prices and improved technology have recently moved these deposits into the ultimately recoverable reserve category.  It's not a matter of a recent discovery, but of reclassification.

A few comments:

Market price and technology do indeed have major impacts on the amount of URR.  Many hard core peakers are so fixated on the ultimate limit imposed by geology that they ignore or reject these shorter-term, but still very important, effects.

If this "deposit reclassification" scenario is accurate, then I think it makes an overwhelming case that the Saudis have manipulated the markets on a grand scale.  That also makes it a strong argument for data transparency, not that I think we'll ever see much of an improvement over the current situation I that respect.

We have no idea what kind of oil this is, assuming it even exists.  If it's light, sweet then it won't become a factor on the market until the extraction and transportation infrastructure is in place to bring it to market.  That probably translates to a delay of several years.

If it's heavy, sour then in addition to the extraction and transportation buildout, we'll need changed or new refineries, which will add more time (years, I'm guessing) to that delay.

If there's no oil there, then we're back to the "imminent PO" scenario.  If the oil is there, then we will face increasingly tight markets and expensive oil for a period of years, until that oil can be turned into a marketable commodity.  And even then the costs involved might make it expensive enough not to bring down the market price.