Sorry, but that one is TRUE, at least in engineering (trust me, I'm a grad student at Columbia, and you will see almost no american people in the engineering programs; in average, 15% are french - my case - 30% are indian, and 30% are chinese, the rest for some other European or Asian countries, as well as a few North African students + 1/2 american students in each prog. And this actually gets worse when you look at the PhD programs, that are constituted of 75% of chinese students + one or two european student and sometimes one Indian student that gets lost there). Honestly, I won't deny the only reason I got accepted as a master's student at Columbia in 2011 is my french citizenship ; with the exact same application, if I was American, I would not even have been considered for an interview.
The ones I hate most:
"Oh you're applying for PhD? Oh, you've got good grades and you're smart, you'll be fine" (isn't is the case of EVERY SINGLE applicant to a PhD program?)
"What would you do a PhD in the US anyway? You should have stayed in France, our master's degree are so much better. Especially for people coming from your school, you should be able to get a good managerial position within 4 or 5 years. It's stupid to try to get more knowledge - and you will be paid with money from my taxes !!!??! - when you can immediately get money" (no comment on that one. That's just super arrogant, proof of immense stupidity, and THAT'S NOT WHAT I WANT TO DO ANYWAY. No wonder we're so bad at anything closely related to research)