An exceedingly late reply here:
It probably isn't too far from the truth, in that they vehemently assure you that there is absolutely no guarantee for funding. That often turns away a lot of good potential candidates to Stanford, too, which can be a boon for others. That being said, I think if you're stubborn and persuasive enough and you have the right skills, you can get funding. I'm funding my own way through grad school after spending a year working, which means I had just enough saved for about 2.5 quarters with rent, not quite enough to get through an entire year. I was looking to be a little more comfortable financially, so I managed to snag an RA-ship for this upcoming quarter, though not in the CS department. That required a lot of work and some amount of convincing, but it's not impossible.
I do agree though, the CS department isn't exactly easy to get into, and it's hard to know what a professor or the department is looking for every year.