What are the chances for a scholarship winner to be denied admission at Uni?
It very much depends on the admissions system. If the system is based (almost) strictly on grades (the way the German system largely is determined), then having a scholarship doesn't help with admissions. This is also the case if there are minimal tuition and registration fees associated with admission.

In the US, though, funding is a much more important issue in admissions. Students with their own funding source definitely have an advantage over other students of comparable quality, since they cost less money, and thereby can be admitted when other students can't. However, a student who has a scholarship but might not be a good fit for the department might not be admitted.