Price feeds are the answer? The price feeds in question don't even track the price of Dai - so I am not even sure what mechanism you have thought up to explain to yourself how Maker works.
If you are still having trouble understanding the system there is no shortage of resources available. Of course if you dismiss the resources because of an anti-cryptocurrency bias as you have then you will end up clueless since this is a realm with low-coverage in the mainstream.
I've read the previous, very long, answer. Yes, it explains how the Maker system works, but it does not explain which parts constitute the Dai to USD peg. The price feeds track the price of Eth, which is used to set the price of Dai if automatic settlement is needed (something I learned from the resources you describe!). If that doesn't set the price of Dai, then what does? Are you suggesting it's an emergent behavior of the system as a whole?
When someone's ethereum CDP is liquidated onto the market it is auctioned off for Dai before the collateral no longer backs the Dai. The price feed determines when a CDP is in need of liquidation. This mechanism is important because it keeps the system overcollateralized.
There is also something called global settlement. This is for major upgrades (they are doing one on the 16th) and also in case of emergencies. The price feeds in this case are used to determine Dai holder's proportional claims to the collateral (using the target price 1 Dai = 1 USD). It may happen happen Dai holders get less or more depending on the circumstance. In addition Maker is a major Ethereum application so if it failed the price of Ether would tumble. That is part of the reason they are expanding to support more collateral types in the update slated for the 16th.
So every Dai is a rough promise for one dollar but that does not answer why Dai is stable day to day. It works like this: When the price of Dai falls under 1 dollar, CDP owners will buy it up and close their positions at a discount which will put upward pressure on the price. Likewise, if the price of Dai goes above one dollar then fresh CDPs will be opened and fresh Dai will be sold on to the market, putting downward pressure on the price. If that isn't enough, the interest rate is manually adjusted to fine-tune the supply.
In the future part of the interest will be payed in to an optional savings account for Dai holders. The idea is that by adjusting the APR the demand for Dai can be fine-tuned. When rates are high people will buy Dai and lock in in a savings account. If demand is too high rates can be lowered causing an inverse affect.
