Pueri debent esse boni
Habitus vero mediocritatis intelligitur esse liberatio hominis a dispositionibus subiectibilibus
Why are boni and liberatio nominative? It seems to me that they ought to be accusative as predicates of the indirect statements after debent and intelligitur.
This is called a nominativus cum infinitivo, which is possible with intellegitur because the finite verb is passive. Debeo normally has a mere infinitive with it, so there is no indirect statement there either. There is no indirect speech, no accusativus cum infinitivo.
An a.c.i. cuts through the sentence, separating main clause from indirect statement, such that we have two praedicates, and the subject of the main clause cannot be a constituent inside the indirect statement:
Marcus intellegit se parvum esse. "Marcus knows that he is small."
The main clause is Marcus intellegit; the word Marcus cannot have any role inside the a.c.i., which is why we need to add a word to be the primary argument of the infinitive (se). It is basically a repetition of a reference to the same person (which is what pronouns are for).
Marcus intellegitur parvus esse. "Marcus is understood to be small."
Here, we need no such pronoun, because it is all a single praedicate, as in your example. It is a 'transparent' construction, one could say, where the subject is 'passed on' from finite verb to infinitive. The structure of the verbal praedicate is best viewed thus:
(Habitus) → intellegitur → esse → liberatio.
Each word 'governs' the next word here: the subject has a finite verb; the finite verb has an infinitive; and the infinitive as a complement. The standard complement of the verb esse ('the thing or property that the subject is') is a subject complement, and subject complements are normally in the nominative in Indo-European languages.
More examples:
Nero videbatur insanus fieri et matrem odisse.
Agrippina dicitur nihilominus filium suum amavisse.
