In which case you move to #2 which (to me) seems much easier to get: A Github or other online repository of your source code demonstrating contributions to open source projects or impressive projects of your own.
True - if the open source project you've contributed significantly to is, say, a well-acclaimed machine learning library, and you're applying to a machine learning Ph.D., then the sum of your accepted pull requests might be a reasonable proxy for a recommendation letter from the (presumably well-acclaimed) maintainers of said library.
It does not seems so to me. To show that your interests align, you do one of the challenges that Jeff lists in part 2. Part 1 is only to show you are a strong programmer/ambitious so your projects can be in anything it seems.
if you do that you might as well forget the PhD. Schools don't want to teach you, they want to accept the best applicants. Applicants who work on open source projects and can get a job anywhere. Applicants that became great learning from somewhere that is not the school that he is applying to. Whereas as a post doc you'll be someone's bitch working for 40K per year. Screw the PhD and whatever it is supposed to mean--that you did all your stupid homework assignments and kissed people's asses for three letters of recommendation and that you "gamed" the GRE.
That is an interesting dilemma, yeah. To be a sharp homework-hammering undergrad is not to be a good researcher & fuzzy situation manager. It's why there's such focus on undergrad research these days, it helps identify the capable people and build their skills (as well as getting some amount of budget help).
The professor at Brown clearly enunciates some of the issues with the current system quite well.
But to make it a meaningful experience (and get out of it with a PhD) you need a wholly different skillset. It's clear that you have never seen a kid who destroyed the productivity of a whole office because he treated his colleagues Just Wrong, and that you have never seen a fellow who just couldn't transfer what he learned in class to real-life application.
That's harmless. But if you have someone who continuously messes up shared equipment, leaving it for the next person to fix, and who won't improve their attitude, no matter how often you tell them, that's deadly for morale.
That's not as true anymore. If you did some interesting independent-research projects as an undergrad, which you got published as conference papers, that strongly overrides your undergrad course grades nowadays, at most schools. Basically publications trump everything, and grades are only used if you don't have any publications.