I did not know this about American citizens, but it seems unlikely. My intuition is quite the opposite: because Ph.D programs are drastically more competitive than master's programs (higher average test scores, GPAs, and lower rate of admissions, at least at my university), my chances of being accepted into a super-competitive program would be more feasible on the master's level.
I'm a Ph.D. student in Computer Science. I originally only applied for Master's programs. I was rejected by all of the schools I wanted to go to. I eventually ended up in a good Ph.D. program, but that was largely by chance.
You're better off applying for a Ph.D. program, then bailing after earning your Master's. It's not good for the school, but it's better for you.
Your understanding of the problem is what's wrong, not your analysis. You're thinking of the Ph.D. pool and the Master's pool as independent of each other. They're not. Funding for Master's and Ph.D. students comes from the same pool, and many programs won't admit students they won't fund. So the question sometimes comes down to, "Do we admit this Master's student or this Ph.D. student?"
Ph.D. students are an investment: they eventually publish papers with the university's name, and in academic settings, the university's name will forever be attached to that person. Master's students often don't publish, and upon graduation are generally not in circles that care about pedigree.
I applied to master's programs because I wasn't sure that I was going to get a PhD. It was a mistake. Top schools don't like master's students, and don't fund them by default. Some professors were confused as to why I didn't apply for a PhD after reading my application. One professor told me to never mention that I wanted a master's degree. Some top schools consider master's students to be a lower form of life than PhD students, and they have to reapply to switch to PhD status. Professors don't take you seriously if you're a master's student. I got accepted into my top choice, but it meant absolutely nothing because there was no funding and little chance of professors acknowledging a master's student's existence.
It's a silly game, and you have to play it right. If you want a master's degree and are unsure about the PhD, apply to a PhD program. If you just want a master's, apply to a PhD program. If you would rather stab yourself than stick around for a PhD, apply to a PhD program. If you want to be treated decently, have research opportunities and perhaps some money, apply to a PhD program.
In a nutshell, if you want to go to grad school, apply to a PhD program.
Luckily I was accepted into a decent school with an assistantship and the ability to switch to PhD if I want to.
