No the thesis is not that the current budget deficit is a problem but the increasing costs of bribing and subduing the populace and the factions of the royal family turn into a bidding war, with increasingly expensive wars as the proxy war in Yemen escalates. The ownership of the assets overseas is somewhat complex too - there is little public documentation, but the country does not really own much, it is owned by individuals, as this is a traditional feudal monarchy, not a modern country, so there is no real "state". At some point with increasing factionalism this could be problematic for borrowing. If there were serious political issues, like the Saud's being kicked out, much of the money would go with them, and the credit rating would not last for long.

On the other hand people have been predicting the end of the House of Saud for decade now, and people have continued to support them and sell them unlimited weapons.