I propose, they had never been trusted. Nations do not believe in trust. At the International Relations level, IR Realism is basically the only generally accepted policy. You may have a few Constructivists, but the smartest ones still put trust and norms below power calculations.
Its really that the average person has essentially no understanding of IR and history.
I assure you that verification methods have been happening. The amount of trust was less than the amount of verification.
Depends on when gold was shipped to the US. For the better part of the 20th century there was absolutely no reason for most of it's friends and allies to not trust the US. Especially if you deposited your gold with the US around the world wars or any time before the mid 60s really.
There is enough incentive for the US to not be transparent about the actual gold that is left.