culture of PhD students

culture of PhD students

I will be beginning my PhD program in a few weeks and I am adjusting to a
lot of changes. Of course, there's the transition from undergrad to grad.
Aside from this, I am pursuing it in the USA with me being an
international student. It's my first time to study here as well.
A couple of days ago, I met a PhD student in EEE. I'm in applied math btw.
I asked her if the PhD environment is collaborative or competitive at the
institution I'm at. She was kind of baffled by my question until I
clarified to her that I was pertaining to the first couple of years when
you take courses and qualifying or candidacy (not the thesis defense)
exams. But still she was intrigued as to why I had to ask such a question
and gave me this reply:
"Come on you're a Ph.D. student. Are you really a Ph.D. student?"
I was not offended but I am curious as to the implications of this. In my
undergrad institution, we rarely had graded homeworks (British system). We
might have some but it's not weekly and it's not a substantial part of
your grade. But I had a professor who gave us weekly homeworks and they
were of course not easy. But when I collaborated with a friend of mine,
which is allowed, I learned much more from the course and we were able to
advance each other's ideas. And I thought that this is good. Of course,
the smart guys in my class avoided to collaborate as much as possible...
So what are your thoughts? Are Ph.D. students really that competitive? Or
are they encouraged to collaborate? What's your take on this?