Salaam
This seems highly unlikely given the Saudis have multiple allies that can supply them IF they need any.
I highly doubt they'd run short one day after the attack. Even Pakistan - a poor country that imports much of its oil - has a few weeks worth of reserves, so I find it extremely difficult to believe that the country with the largest oil reserves and which produces 12% of world total production would run short within a day or two.
Such an outlandish claim - and unless it is varified by neutral sources - and Iranian news outlets and officials are not neutral - it cannot be taken seriously.