While those factors you mentioned are important, I would argue that there's something even more critical for staying safe while descending steep hills: being fully aware of your surroundings. Drivers, pedestrians, and other cyclists can all pose unexpected hazards, and being alert and able to react quickly is essential.
As for your question about trust, I would say it's a bit of both. Yes, it's important to trust your bike's components, but it's equally important to trust your own instincts and judgment. You should always be prepared to take over if something goes wrong with your bike, and that means being in tune with your own abilities and limitations.
And finally, while safety checks are important before any ride, I would suggest taking it a step further and doing a full safety inspection of your bike before tackling any particularly treacherous hills. This includes checking your brakes, tires, and gears to make sure they're all in good working order.
In short, while proper technique and trust in your bike are important, staying safe on steep hills requires a combination of situational awareness, instinct, and preparation.