It's not just brake dust from your car. It's brake dust from cars in front of you, what fragments of metal that you see as dust get kicked up from behind your car. Basically, it's dirt and dust made of metal that end up on your car, but they happen to be so sharp, they embed into the paint. Now, it doesn't fully puncture the paint. That would just be silly. Just far enough in to resist washing, but you could probably pick them off with your nail. After being stuck in the paint, the contaminate rusts and that's what you see.
They're not so deep that you could remove forcefully with say a plastic card, but obviously you would never want to do that since it would cause major scratches to your paint, hense why a clay bar was developed. I assure you the dealer for once is not making this stuff up, and it's a very common paint contaminate.
If you're serious on diving into the detailing world, you'll be amazed on the levels of "clean" exist. Next class, topic on removing fine scratches, dead, and oxidized paint.