Are the infinitives that follow catenative verbs considered object?
Solution 1:
He flatly refused [to discuss the matter].
My brother refused [to allow anyone to help him].
He has steadfastly refused [to answer my questions].
The whole point of the catenative construction is that the non-finite clause functions as catenative complement of a catenative verb, not as direct object. The catenative verbs concerned are thus functioning intransitively.
"Refuse" can be transitive, as in "He refused my offer of help", but in your examples "refuse" is intransitive in a catenative construction, and thus there is no direct object.