Growing up in a world where money tends to travel digitally rather than physically gives a bit of a different perspective on things. To me, the money in my bank feels more 'real' than physical paper money, because the money in my bank is what I tend to buy things with and what I use to pay for bills. Because of this, I'm going to flip things around and try to explain BitUSD from a perspective that I don't think has been explored yet:
BitUSD is pegged to the USD because it says it is.
That may seem a little hand wavy, but the social meme of a perceived value from branding is a lot more powerful than people tend to assume. Take paper money. There's no reason a $5 bill has to buy the same amount of stuff as the abstract concept of '$5'. You could just as easily walk into a grocery store and find that you can purchase 2 loaves of bread for $5 sent through your debit card where a $5 paper bill might only buy you a single loaf of bread. This rarely happens, however, because the expectation that others will value the $5 paper bill at $5 motivates people to treat it as being worth $5.
With bitUSD, the expectation that 1 bitUSD will be worth 1 USD keeps it at equilibrium. If people sell their bitUSD and the price drops, then this will trigger investors to buy, as they expect the long term value to be larger than the current value. This, in turn, drives the price back up. If people buy enough to push the price above 1 USD then this triggers sells, as the current price is higher than the perceived value. This, in turn, drives the price back down to its perceived value. This is called a 'nash equilibrium': The value of something that is arrived at by the actors in a system because of the perception that the other actors will arrive at the same value.