This actual study itself has at least one very good point that may not be obvious to people: our leadership's drive to promote the idea of a STEM shortage is primarily to justify guestworkers and allow them to add provisions like
OPT-STEM extensions. Don't get me wrong, there is a sort of shadow brain drain war going on here that for a long time the West had easily been winning. UK, Germany, USA, etc had been sucking up the talent from India, China, Russia, Ukraine, Turkey, you name it we took the brightest from it. And it was really really easy. And now Western leaders are kind of getting uncomfortable because, well, it's not really working in our favor anymore. I care that our politicians are being deceiving about this concept but I don't care about the "taking our jobs." In fact, I'm one of those meritocratic boogeymen that thinks our borders should be open with nothing more than a background check into your criminal record before you're granted entrance to the United States. Sure, some other stuff would need to change but that's an entirely different argument I'm not going to get into.
The main point of this study, however, is what the Post picked up on and is being reiterated: there is no shortage of STEM workers here in the US. And while that's likely true, the study (though comprehensive) doesn't really seem to ever step up to the plate and look at STEM versus non-STEM in the cases of employability and what those industries do for our GDP. Our leaders like Obama are operating on the assumption that a surplus in STEM workers is better than a perfectly equalized workforce with zero unemployment. They're not going to say that but my guess is that they're getting uneasy that China is mandating how many STEM workers it will produce and limiting the number of liberal arts degrees. The West is now uneasy that they might start losing the STEM war and they're trying to figure out how to scare their populations into letting them selectively brain drain other countries. A fake "massive shortage of STEM workers" is pretty much their only card so far.