A fact is not something "assumed" true - a fact is something which is true. There are objectively true facts; we just have to discover and appreciate them.

There's a difference between something being a fact and something being accepted as fact. The former is an objective statement of reality, whereas the latter is based on our individual perception and understanding of that reality. It's necessary to be consistent with your definitions because people may be discussing different things.

Pure democracy does not determine facts, because only existence does that. However, some form of that principle can help determine what we should accept as true (e.g., evolution being universally accepted among the academic community).