Like I said, I did feel at a bit of a disadvantage. I double majored in English Literature and Math at the undergrad level, which is not something you would typically do in Europe or Asia. Even if you stick to a single major, the US system typically requires a lot of general education coursework (history, art, etc). I studied plenty of math, but European and Asian students typically focus much more intensely on their major subject at the undergraduate level. I had met the prerequisites for some of my grad courses, but it was still new material for me. For many of my fellow students, it was review.
As the percentage of US students continues to dwindle in US based graduate programs, I think that these courses will be increasingly taught assuming a European or Asian style undergraduate experience (ie., earlier specialization) - after all, that's becoming the typical background in these programs. I don't think that the US students necessarily lack the talent or core prerequisites, but they will be more likely to be seeing "graduate level" material for the first time, whereas it may be review for the international students.
To give an example, suppose there's a graduate course in advanced stochastic processes, and prerequisites are calculus based statics and an undergraduate course in introductory stochastic processes. The American took the prerequisites, and also took a lot of coursework outside his major (as required by his university). An international student took far less coursework outside the major and instead used the time to take what in the US would be graduate level courses in stochastic processes. The international student, in this case, would be at a substantial advantage.
The American, though, will probably choose some other path than a PhD in a STEM field - I personally that the RAND study has pretty much identified why that's the case (better pay and prospects in other fields). I think your insight into the difference between US and international students around markets is a good one - if your failure rate is higher, you'd be more inclined to avoid that program, so they are responding differently. That said, I think that the difficulty of gaining admission to professional schools in the US is a also a major factor (medical and law schools make it far more difficult for international students to gain admission than PhD programs in STEM fields, and if we go the "staple a green card to any STEM degree" but don't take comparable actions in other fields, we should understand that this will probably exacerbate the trend away from STEM and toward other fields among people who can choose their profession in the US).
Oh lastly, to answer your question - yes, the dropout rate from STEM undergraduate majors in the US is high (new york times did an article on this recently), and my undergraduate program was no different. But those Americans who make it through often go to professional schools or into finance (though the trend toward finance has reversed somewhat recently), again (I believe) for the reasons specified in the RAND study.