Given time and privacy much can be accomplished.
Under ordinary levels of supervision for someone in such a facility, much less the supervision such a high profile prisoner should have had, he should not have been able to make such a rope because he would have been denied the time and privacy needed to do so.
The whole situation stinks on ice.
I don't think he did... I know roughly what those paper sheets are. Considering 2 twin size sheets (bunks), the time it would take and the tools necessary to cut thin strips, turn those strips into cordage, and then turn the cordage into rope - enough rope to do the job, seems entirely unlikely.
Even if there were blankets - a far better material, just how would he cut the stripping? You are talking about maybe 1/4" maintained across the entire length of the sheet. Then two of those strips have to be rolled together across the thigh, making round, slightly stronger strips... You will lose a quarter to a third of the length in this stage...
Then the rolled strips have to be fashioned into cordage... losing tons of length... Even using a three-strand, two-forward-one-back braid - about the simplest tensioning braid (tensioning braid increases strength), You're talking hours and hours just to make the cordage... and then repeat using three-strand cordage to make the rope... And that rope would be mighty thin... Maybe strong enough... So maybe even repeat again using two or three strand rope to make better rope... The time that takes is immense. As is the material.
And that all depends upon him having been a good boy scout at some time in his life to know how (including splicing, which I have not even approached)... Making rope is hardly a standard knowledge anymore. Making 6 to 8 feet of rope is a chore.
I think it highly unlikely that a world-hopping playboy would know that kind of thing.