Do international students have a lower chance of getting accepted in STEM-fields PhD programs at US universities? The reason that lead me to ask about this is the following paragraph I found on this page (some guidance written by a STEM-field professor at CMU for applying to grad school), he says,

I'm not a U.S. citizen -- how does that affect my chances?
Unfortunately, if you are not a U.S. citizen and you don't hold a green card, your chances for admission are very significantly reduced. One simple reason is that we get an overwhelming number of applications from overseas. The extra work and time we spend on cultural acclimation and language skills for these students means that we can only accept a few of them, and of course this is a very few out of a huge application pool. If you already have a degree from a U.S. institution, that helps considerably with this issue. Also, it is more difficult to obtain funding for non-U.S. students, and so further increases the effort required to bring them here. Historically about half of our department's graduate students are non-U.S., although that proportion tends to be closer to one quarter in my research group.

The bold italics are mine. I personally find the &quot;cultural acclimation&quot; argument utter nonsense, and the &quot;language skills&quot; seems even more nonsensical, since almost all programs require quite good TOEFL/GRE test scores. So I suppose my question has two components really, and it concerns PhD programs specifically:

Did you experience difficulties funding a student in your department (STEM field) solely because he was a non-US citizen? If so, does this influence your decision of admitting non-US citizens?

Does your department has a specific quota of non-US citizens to be admitted?


Edit: In light of the new statistic I found, it seems absurd to say international students (i.e. non-US citizens) have a hard time getting accepted, especially in ECE. I think the professor's remark above doesn't reflect the bigger trend (he is with the ECE department at CMU), and his research group (where the proportion of international students is about 25%) is more of an exception to the &quot;rule&quot;.
Since you can't change the situation and suddenly discover your US citizen parents, you can only apply for positions and make your best case. As I mentioned in comments, the quotes are from an individual who is clearly expressing an opinion, not the results of research.
Yes, you will find people who will mark you down a bit or a lot based on your circumstances, but you will also find people who take a broader (and IMO, wiser) view that applicants are individuals who should be evaluated on a relatively fair basis.
But, you will find that competition in some fields and in some universities is intense and you have to make the case that you are an excellent candidate with many expectations of success.
Note, that some parts of the article that you didn't quote are more general. The writer is correct that funding in the US for doctoral study is normally not a problem as nearly everyone has a position as either a TA (most common) or an RA. This provides sufficient funds to live (if a bit humbly) and pays all tuition and fees. While the funding may not come from the professor, it is almost always available to anyone who is admitted and who requests it.
Visa problems may be intense at the moment as is the difficulty of travel, but those are outside what can be advised here.
What matters, much more than trends, however, is what it means for you as an individual. If you present an excellent application, showing hard work and past success and people are willing to write you good (great) letters of recommendation, you will have a chance.
But don't apply to too narrow a range of institutions. Give yourself flexibility and backup.