grammar - Why does "An Advanced English Syntax" say the infinitive in these sentences is adverbial?

In sentences like the following the Infinitive is probably Adverbial, and therefore the italicized part will be put in the Adjunct column.

You seem to be ill.

He is known to be reliable.

It was felt to be very unkind.

(p. 22, An Advanced English Syntax, by C. T. Onions, 1904)

They use the word ‘probably’ to describe those as adverbial (no further information). The book has no grounds why they function as adverbial. Albeit it is a traditional authority (1904), I have a yen for the authors’ intentions. I’m not sure whether today English grammarians can say that they, the infinitive phrases, function as adverbial complements. I was told once that infinitive complements after 'seem', 'feel' are adjectival, modifying the subject (He seems to be happy, he to be happy). My conjecture about why the infinitives are described as adverbial is that they think Infinitives after copular verbs modify the verb, not the subject, to complete the predicate. i.e., What modifies the verb is adverbial (what modifies the noun is adjectival). What do you think of that?