> So in essence, this means that how fast and how well a connection to an Internet site actually works, is in danger of depending on that site's actual content, not simply on its own hardware, Internet connection, and popularity?

No, it's whoever ponies up the cash for the telcos.

That said, businesses usually reserve the right to do business with whom they choose, so if this door were opened, it could easily lead to the telcos choosing to refuse to do business with providers of content they don't want to support. I'm not a big fan of slippery slope arguments, but the first step is wrong enough all by itself.