Admissions requirements and research expectations for graduate students vary wildly across different disciplines, subfields, countries, individual departments, and even individual advisors. I would be surprised to discover a PhD program that actually required prior publication before admission, but at least in computer science, it is a fact that strong PhD programs regularly attract applicants who have already published.
In particular, students are much more likely to produce publishable research in a Master's program than they are as undergraduates. Again, I'm unaware of any Master's program that requires publication as a condition of receiving the degree, but a good Master's thesis is publishable, and Master's students do regularly publish.
Strong PhD programs are looking for students with potential to become good researchers. Nothing provides evidence of potential for becoming X better than demonstrating that you already are X. So PhD applicants whose have published good research (in a reputable and visible venue) have a significant advantage over applicants who have not.
The absolute best PhD programs in a particular subsubfield, especially if those departments are small, attract enough published applicants that a significant fraction of their PhD students had publications when they applied. (For example, theoretical computer science at Princeton.) But even in those departments, I'd be surprised if "a significant fraction" was a majority.