
James W. answered 04/17/19
Highly Certified Translator and Interpreter
I think you've identified the two main ways という is used:
1). A specific person said this.
2). Society/general knowledge/common sense says this.
I'm sure you've seen examples of the first usage - たけしは「今日雨がふる」といった。/ Takeshi said "Today it will rain." So for the first usage, we're literally reporting what someone said (usually in the past tense).
The second usage is where I believe you need a little more context. From the eyes of a native English speaker, there's no real difference between
> 彼が金を貸してくれたということは私は彼に信用されているということだ。
and
> 彼がお金を貸してくれたことは私は彼に信用されているということだ。
There's no real difference in the information conveyed in these two sentences. So why add という?
The answer is that the first sentence is how a native speaker would actually talk. The という softens the statement, makes it less direct, and just generally "sounds" better.
Let's look at the other example. 「今日のテーマは愛という事だ」 is less direct - more poetic, you might say. 「今日のテーマは愛だ」 conveys the same information, but with less class and tact. It's too direct to sound good to a native speaker.
So to sum up, for the second main usage of という, no additional information is added to the sentence. It is simply a means of making the sentence sound 'better' or 'more proper'.
Hope this helps!