You're missing the point, and your example for failure--which is highly, highly unlikely--could just as easily apply to ebay, so your argument is completely illogical. Also, Facebook is not an internet provider. Are you really that ignorant?
Do you think the average citizen recognizes that ebay owns paypal? Not likely. Facebook is likely going to expand far beyond being an internet social network. That'll be what people associate the name with, but just like ebay, much of its growth will come outside of the social networking site; that is, if they play their cards right. Think mobile. Think operating systems. Get out of the social networking mindset.