I think Goshin summed it up nicely. Basically trust is on a spectrum, really it's just a subset of truth. What he wrote, the way I interpret it, is that trust is kind of irrelevant. It's just a convenient short-hand label that helps us save time.
Take your example:
1. Do you trust the driver on the other side of the road, to stay there?
- Which is actually just a question of science, specifically "Do you believe it is true that, in the near future, the car on that side will stay there?"
It's important not just to show that it's really a question of "truth" underneath, but it also highlights how it's NOT some personal idea of trust. Point being, the driver may be the best driver, the most "trustworthy" driver EVER. But the car perhaps could malfunction to end them in your lane. i.e. trust, is irrelvant.
As a truth statement, we go right back to how one determines what is, and is not, true. Most of us use a combination of instinct, evidence, experience, measured via probability, vs the time we have to make the choice, the potential reward, and the potential risk. That's how we gauge trust...because it's really just truth.
I don't really see that as subjective, I see it as reasonable. Did you have a different notion of trust in mind?
There is a psychological issue here as well. Worrying about outcomes can be stressfull, most people hate serious decisions and avoid them with all sorts of tricks like denial, ignorance, alcohol, etc. As a result, they sometimes convince themselves trust can be obtained in some other way.
Another psychological aspect is when you communicate you are confident in someone, that added vote of confidence *may* help to keep them trustworthy, or at least more so than without showing confidence in them. Is that trust, or manipulation?