> 1) Throw away fine detail by discarding high frequency components
The reason it works is that fine detail is almost completely correlated across colors, so if you only keep the Y plane at full resolution it still stores it.
You couldn't just throw it out in RGB space because eg text would be unreadable.
In terms of understanding how JPEG compression works, and how it relates to human perception, I'd say that in order of importance it's:
1) Throw away fine detail by discarding high frequency components
2) More heavily compress/discard color than brightness detail (using YUV)
3) Quantize the frequency components you are retaining