というのは事実だ means "it's true that", "it's a fact that": the clause before it is presented as a claim, and confirms it. It follows a plain-form sentence, and a noun or な-adjective needs before という: ×優秀というのは事実だ.
。
It is a fact that global warming is getting worse.
。
It's true that the population is falling.
きごう?
Is it true that many people were hurt in that accident?
Most often the fact is granted before a "but": the speaker admits it and then says why it does not settle the matter. or follows 事実だ.
、。
It's true that he worked hard, but he got no results.
、。
It's true that she is very able, but she doesn't have much experience yet.
says a claim is untrue, often a rumour or an accusation.
says a claim turned out to be true.
。
It is not true that he stole the money.
。
It turned out to be true that there used to be a river here.
without いう means the same; という frames the clause as something said or claimed before confirming it.