This is amazingly bad statistics.
The author is using self-reported surveys of STEM majors who didn't work for an SV company to answer the question of what SV companies are looking for. There are giant assumptions: 1) they wanted to work for an SV company 2) they're not deluding themselves about why they didn't get offered an SV job. A much better source would be to actually ask the SV companies why they didn't hire someone.
As someone who has been actively hiring for the last six months, trying to grow our team from 5 to 10, hiring is really damned hard. You'll get a mountain of crappy resumes, and a few really good resumes. Some of the really good resumes will turn out to be really good people, some of them will accept offers somewhere else, and some of the people that initially appeared great will test poorly, or you won't click with them personally, or something else.
Aside from technical ability, startups also need to look for a certain personality. At my own company, we're strongly influenced by the Valve Handbook. We like to hire people that understand the problem on their own and say "I think this is the most important thing to work on". Not every STEM major has that capability. We also like to hire generalists, or people who aren't afraid of learning how to do the things that need to get done. Both of these reduce our hiring pool.
I know founders of funded SV companies who aren't in the country legally. One in particular has a pHD, published papers, and is quite literally creating jobs. The O visa is a possibility, but it's a ton of paperwork. The H1B is tricky to use for founders, because the visa requires that their "boss" be able to fire them. Also, the H1B window is short, and the next opportunity to hire someone on an H1 is something like Fall 2014.
I've not given offers to candidates because their visa situation was too risky. As in "I'm in the country legally today, but I have to go back home for a few weeks, and I may or may not be able to get back in".
Every company I've talked to is in a similar situation, in terms of being desperate for hirable, highly skilled engineers, at any price.