Here is a relevant example where the present passive infinitive vivi is interpreted in an impersonal context after a verbum dicendi (negat) like in your examples above:
Negat Epicurus iucunde posse vivi, nisi cum virtute vivatur. (Cic. Tusc. 3, 49)
NB I: I've just found a nice variatio of this example in another work by Cicero, but this time with an indefinite subject: cf. the impersonal construction(s) above with At negat Epicurus -hoc enim vestrum lumen est- quemquam qui honeste non vivat iucunde posse vivere (Cic. Fin. 2.70).
Pinkster (2015: 270) gives some examples of your "non-problematic" type (i.e., with a perfect passive infinitive) in Section "5.21 The impersonal passive". E.g.:
Nunc tu, Cleostrata, / ne a me memores malitiose de hac re factum aut suspices, / tibi permitto: tute sorti (Pl. Cas. 393-5).
He also gives some examples of the future passive infinitive (supine + iri) in a subordinated impersonal context. E.g., cf. also 1(δ) in this link:
Ipsi vero nihil nocitum iri inque eam rem se suam fidem interponere (Caes. Gal. 5.36.2).
NB II: A similar example with the present passive infinitive noceri is given by Pinkster (2015: 270): namque ea materies (...) reicitque eius (sc. ignis) vim nec patitur ab eo sibi cito noceri (Vitr. 2.9.14). Here is another one: (...) pugnatumque ab hostibus ita acriter est ut a viris fortibus in extrema spe salutis (...) pugnari debuit (...) (Caes. Gal. 2.33.4)
Finally, take a look at Woodcock's (1959: 43) Section "60. The Impersonal Passive", where the following examples of present infinitives can be found:
Mihi numquam persuaderi potuit animos emori 'I could never be persuaded that our souls died' (Cic. De Sen. 80).
Vult sibi quisque credi 'Each man wishes to be believed' (Livy 22, 22, 14).
SOURCES:
Pinkster, H. (2015). The Oxford Latin Syntax. Vol. I. Oxford: OUP.
Woodcock, E. C. (1959). A New Latin Syntax. London: Methuen.