Foreign "undergraduate pedigree" and applications to PhD programs

A reader writes:

I'm an undergraduate student of philosophy from Brazil and I would like to ask you some questions if you don't mind. I know the issue I'm going to raise has been discussed at other places, but I really don't know how to proceed in my case. My concern is with to what extent "undergraduate pedigree" affects international students applications. I've read commentaries about this issue, but they are mainly focused within universities in the US and I'm not sure how exactly those considerations apply to international students. I mean, it is not uncommon to find international students under graduate student lists who have graduated in their home country and are now attending ranked PhD programs.

So, my question is: if the so-called "undergraduate pedigree" is so present as some would claim, how come those students get admitted to the programs? I will be applying in the next year and it would be really helpful to hear commentaries on this issue to evaluate on more solid grounds my chances of being admitted.

Advice from readers?  It would be particularly good to hear from admissions committee members and from students (there are, indeed, many) who came from abroad to the US for graduate study and with great success.   Signed comments preferred, but even anonymous comments must include a valid e-mail address, which will not appear.