The air is full of dust. It's floating around everywhere all the time. When you open the lens in a dusty environment (which is to say "every environment that isn't a clean room"), dust gets into the light-box of the camera.
You didn't ask, but this is why seems silly to advise people to point their cameras down while changing lenses. Observe how dust moves in the air: it falls down gradually, eventually, but mostly it responds to air currents going up, down, left, right, wherever. If you're in an especially dusty situation, the important thing is fast.
The risk isn't really that dust might fall right on the sensor while it's exposed. It's that dust floating around will eventually settle there and stick. As the question you link notes, the shutter itself doesn't protect much against this, since it opens "violently", scattering dust around.
In fact, arguably, the larger mirror box in a DSLR is just more space for dust to drift around in waiting to cause a problem. I don't know if that's a real-world issue, though. In my experience, the automatic dust-removal systems all cameras now include have become very good in the last decade.
The one thing I know for sure is that having the sensor closer to the opening makes it easier to clean once some problematic dust does build up. So, advantage mirrorless for that, at least.