If this suspicion existed then you'd see a spread between (gold price in the US) and (gold price outside the US)
When Trump screwed with the tariffs we saw exactly that. Arbitrarily messing with tariffs is one of the risks that causes people to think keeping gold in the US is not entirely safe.
Not necessarily. If relations are good, people are willing to look the other way a lot.
Either way, you aren't left holding the bag, you're giving the bag to speculators.