The passive that begins with 'It is thought' and past tense

Today doing some English grammar exercises I stumbled upon the two examples in The passive section:

It is believed that the children had been hiding for two weeks.

It was thought that the book had been destroyed.

The thing that puzzles me much is the usage of Past Perfect in the first sentence

had been hiding

and, probably, in the second sentence

had been destroyed

I had been searching over the Internet for several hours without any comprehensive answer found.

Would anyone please give a reference to the rule that explains the usage of Past Perfect in constructions like that?

The other related case is the following:

The athlete was alleged to have cheated

I'm sorry for what I said. I was trying to be funny. It was supposed to be a joke

The book was thought to have been destroyed

Why can't I say respectively the following:

The athlete was alleged to cheat

It was supposed to have been a joke

The book was thought to be destroyed

I'm able to easily find the rules on more simple constructions like It is thought that ... + Present Indefinite / Present Perfect but no comprehensive sources on similar but + Past Perfect

The book with exercises is highly recognizable btw but it doesn't give the answer

Thanks