By that time, gold redemptions were mainly available only to foreign entities. Unlike all other forms of money[1], only US federal government spending, in cooperation with the Fed, could create new reserves[2]. That there were too many reserves in foreign hands chasing $35 an ounce gold could only be the result of US federal spending. Therefore while foreign demand was the proximate cause, it was definitely a downstream consequence.

The size of the US government's outstanding liabilities at the time isn't relevant, what affects prices is money flows, not stocks.

[1] https://en.wikipedia.org/wiki/Money_supply#United_States

[2] Back then the Fed wasn't willing to just expand its own balance sheet significantly on its own initiative as it is now.