As a CS PhD student, I have asked this question before of professors on the admissions committee.
Once the applications come in, they sort them into 3 separate piles: US, India, and China. Each pile is evaluated separately, because they aren't comparable. e.g. grades and prof recommendations from the US matter a lot, whereas from China, it's hard to compare grades and prof recommendations are almost always fraudulent. (I don't know what differs about India.)
Then they accept the top ones from each pile, and try to overall choose the top students across all piles. So it's hard to compare "maybe accepts" from different piles, but they do their best.
I guess other countries (besides the big 3) get treated differently because they are more rare.
So, basically, the answer is no, being US based does not really help or hurt you.
I have heard that you have to be extremely good if you're Chinese, because if you're not, it's just too hard to compare you to people from the other piles reliably.
Obviously, this story is highly anecdotal. I'm sure other departments have other ways of handling the problem of compraring people from different educational systems.
Speaking english is a certainly a plus, but it seems outweighed by all the other benefits to the advisors that a foreign student brings.
(Full disclosure: I'm an American who's going to apply next year to PhD programs.)
But, more likely to be pressured by their family into a "prestigious" career that they aren't really interested in, more likely to have the additional pressure of supporting a wife and be thinking about kids, more likely to be unable to learn how to write research papers well in English (this is surprisingly hard)...
Also, I've definitely seen people from abroad use American grad school as a temporary stepping stone to get a job at a big company (like Microsoft) that will deal with the visa stuff. Not saying they were planning it all along, but it happens.
Of all the above, I think the "being able to write polished, professional, technical research papers" is by far the biggest risk factor that neutralizes the benefits of foreign students that you mentioned.
It feels like the main difference here is that the admissions committee looks for evidence of high/low English proficiency. There are also plenty of things other than grades to look at -- test scores, research experience, interests that match faculty here, etc.
That said, how do you judge the English proficiency of someone from India or China, without meeting them and working with them?
They make them take standardized tests that show very basic English skills, but I think you can't really judge that well in terms of doing high-quality writing and good interpersonal communication.