If I'm understanding you correctly, the innate value of precious metals will (in theory) go up as the trust in the dollar goes down. Is that right?

I've never quite described it in that way, but yes, that's more or less what I believe.

It's scary to imagine what will happen if the dollar experiences a serious long-term decline in value - so many people in my family and friends are fully reliant on USD.

Yeah, it is scary. If you earn dollars, have savings in dollars, a pension, annuity, social security, bonds, or other dollar-denominated assets, I think you'll see a significant decline in your purchasing power. The groceries that cost you $100 today, could cost $200 in a few years.

The average person is already stretched to their last dollar, so one can imagine what that would do to them.