What does a Honours degree in India mean? I'm not sure what you mean by a "BSc" system, because in Canada, our undergrad degrees are also called a BSc but it's a 4-5 year program. In Canada, an honours BSc degree usually means the student has taken:
(a) more courses (An honours physics student takes about 10% more credits than a physics major)
(b) maintained full time status
(c) no failed courses, maintained some minimum GPA (my school was 68%, usually not a problem)
(d) usually an extra requirement in 4th year: either a year long thesis/independent research course, and/or enrol in graduate level courses
In Canada and maybe the US, an Honours BSc is usually a different thing than a BSc with Honours standing. The latter case usually means you've graduated above some percentile.
So, if your friend has an Honours degree like above, it would really help them get into graduate school. However, it could be really hard to get all the courses to the North American 4th year level and get some research done as well in only 3 years! Also, is a 3 year degree program in India more advanced/more specialized, so that the material in a North American 4-year program is covered in just 3 years?
I think the reason why you have problems finding this information online is that there are so many different systems across the world and these special cases are on a case-by-case basis. I would assume that the default status is that schools expect students to have an equivalence to a 4-year BSc. If the school does not explicitly say that they will take 3-year degree students, your friend will have to make a case for him-/her- self and prove that they are at the same level as a 4 year degree program.
The bottom line is that graduate students cost a lot of money, especially International students like us. If your friend's 3-year degree does not prepare them for a US grad school, they will probably have to take extra time and (undergrad) courses in the US to catch up, which ends up costing the department more money. Unless your friend shows a lot of promise/skill/etc. it's just not a good investment -- why take someone who still needs training when you have a lot of other applicants with a 4 year degree equivalency.
As for contacting schools directly, I found that most admissions secretaries won't answer many questions before you submit an application because there are just too many variables -- they don't have enough information to give you an accurate response. However, you can't just send them the application information because they don't have time to process applications that aren't sent through the normal system. So, you will likely just get very general responses (e.g. something like "we will accept degrees that are equivalent to a 4 year US BS").
Finally, US grad schools are direct-entry PhD, it's a long commitment: 5-6 years! It's already hard enough to prove yourself a worth investment doing a 4 year degree, so I can't imagine being able to do that in just 3 years. I know in England, like in Canada, a Masters degree is a completely separate degree than a PhD -- in Canada, we do a 2 year courses+thesis masters followed by 3-4 year PhD program (the PhD and MSc degrees can be done at different schools). In Canada, the Masters program is fully funded, just like PhD programs -- Masters students in Canada are treated by their school the same way a US school treats their first and second year PhD students. However, Masters programs in the US are usually unfunded!
So, maybe your friend should consider applying to Masters programs in Canada or other funded countries. It will give them the time, training, and experience to prove that they will make a successful PhD student. It's important to keep in mind that if your friend has their heart set on a US PhD program, these programs tend to start everyone at the same level (i.e. back to first year grad school), no matter if you have a Masters or not. So, a Masters might help boost your application (if you did well/accomplished a lot) but it probably won't be recognized at a US PhD program (even if the masters is from a US school).