> This is logically flawed. It is entirely possible that by
  > removing the barrier of bachelor's degree, they will
  > receive even more applicants who cannot program
  > (percentage-wise).

While certainly true, this line of reasoning works a lot better for big companies than small-ish start-ups. Remember: requiring a CS degree acts as a filter with a certain probabilistic efficacy given that CS degree and engineering ability are correlated but distinct.

If you get 10,000 applications a year (as enterprises like Google, Facebook, and Apple do), you don't really have to give a damn about your false negative rate. Go ahead and install severe formal requirements (e.g., needs CS PhD) -- you're still going to get a number of applications that is sufficiently large to statistically guarantee multiple highly suitable candidates, and you'll save tons of money and time in the process.

Non-behemoths can't really afford many false negatives because the applicant pool is far more limited. False positives at the CV/formalism stage are relatively easily filtered at the interview stage due to, again, smaller volume.