No, they are both incorrect. The Passive is used when you either don't want or can't name the doer. If you write He is not believed to have been rich then by nobody is just redundant.
Sure, you can often see sentences with ...was done by Mr.X. Let's take an example.
1. Jack totaled his father's car.
2. Father's car was totaled by Jack.
They both seem to have the same info. The difference is in what you choose to present as the main info. The main info is usually at the end.
In 1 you tell what Jack did.
In 2 you tell who did it. So here naming the doer is justified.
I hope it helps.