The best argument for low oil prices crashing the US economy would be in any changes to US debt interest rates. While this would certainly change a lot about US politics and finances, one could not count on continuing to borrow indefinitely at sub-inflation levels, America could almost certainly pay it off if it found the will to do so. The fact that America has a large and diverse non-oil economy that would be strengthened by dropping energy prices is certainly a factor.
KSA meanwhile is a rentier state, with 67% of the budget coming from oil sales. Their non-oil economy is badly underdeveloped, and they depend almost entirely on oil money to keep their population fed, occupied, and suppressed. You’ll notice that I said “occupied”, since at a first glance the Saudi economy doesn’t actually include Saudis; 2/3rds of those employed in KSA aren’t Saudi (90% if you exclude oil), and only 30-40% of working age Saudi’s in KSA either have or want a job.
If the oil money were cut off from KSA, the lifetime of that regime would be measured in hours.