That doesn't make any sense to me. Under Bretton Woods, a "dollar" was a contractual equivalent to a fixed amount of gold. There's no difference. When people are talking about "flow out" they're not talking about literally motion of currency[1], just who owns it.

[1] Which is backwards in your reasoning anyway. If you're a foreign power wanting to hold dollars, and dollars are physical gold coins, then you quite literally need to move them physically out of the country, right?