Look at these sentences:
He admitted to have been arrested last year.
The applicant has not admitted to having been convicted of this misdemeanor.
Police say both subjects appeared to be under the influence and admitted to having been using meth.
Finally, 5.6% in our sample admitted to have been using substances to improve muscular-mass or athletic results at least once in the past.
There apparently wasn’t a problem until there was a problem that now has been admitted to having been made up.
Later admitted to have been made up in the 1960s by the vicar of St Olave's Church, Gatcombe.
Three of them use having been; and three of them use have been, but the situations seem to be the same, no? Is it because some of them are clearly placed in the past? What's the difference in their meaning? What kind of grammatical construction is that?