When I messaged Koichi about this, I was given the impression both sentences can mean the following:
一人 じゃありませんでした = 1) It was not one person and 2) I was not alone
一人 でした = 1) It was one person and 2) I was alone
I think it comes down to context. If it’s obvious your talking about yourself, then the second answers apply. If your talking about someone else then it’s the first. I might be wrong but that’s the way I differentiate the two.
In the cases of the Anki cards, I think he’s just given the most popular answer. Although, he really should state this in the next TextFugu update so this doesn’t confuse people.