Assalamu Alaikum wa Rahmatullaah
the sheikh on peace TV didnt recite that ayyat, however check this out:
TAFSEER SURAH WAAQI'AH VERSE 79:
Ibn Jarir narrated that Isma`il bin Musa said that Sharik reported from Hakim, that is Ibn Jubayr, from Sa`id bin Jubayr, from Ibn `Abbas that about:
[لاَّ يَمَسُّهُ إِلاَّ الْمُطَهَّرُونَ ]
(Which none touches but the pure ones.) he said, "The Book that is in heaven.'' Al-`Awfi reported from Ibn `Abbas about:
[لاَّ يَمَسُّهُ إِلاَّ الْمُطَهَّرُونَ ]
(Which none touches but the pure ones.) that `the pure ones' means: "The angels.'' Similar was said by Anas, Mujahid, `Ikrimah, Sa`id bin Jubayr, Ad-Dahhak, Abu Ash-Sha`tha' Jabir bin Zayd, Abu Nahik, As-Suddi, `Abdur-Rahman bin Zayd bin Aslam and others. Ibn Jarir narrated that Ibn `Abdul-A`la said that Ibn Thawr said that Ma`mar said from Qatadah about:
[لاَّ يَمَسُّهُ إِلاَّ الْمُطَهَّرُونَ ]
(Which none touches but the pure ones.) that he said, "None can touch it, with Allah, except the pure ones. However, in this life, the impure Zoroastrian and the filthy hypocrite touch it.'' And he said, "In the recitation of Ibn Mas`ud it is: (مَا يَمَسُّهُ إِلَّا الْمُطَهَّرُونَ) (It is not touched, except by the pure ones.) Abu Al-`Aliyah said:
[لاَّ يَمَسُّهُ إِلاَّ الْمُطَهَّرُونَ ]
(Which none touches but the pure ones.) "It does not refer to you, because you are sinners!'' Ibn Zayd said, "The Quraysh disbelievers claimed that the devils brought down the Qur'an. Allah the Exalted stated that only the pure ones touch the Qur'an, as He said:
[وَمَا تَنَزَّلَتْ بِهِ الشَّيَـطِينُ - وَمَا يَنبَغِى لَهُمْ وَمَا يَسْتَطِيعُونَ - إِنَّهُمْ عَنِ السَّمْعِ لَمَعْزُولُونَ ]
(And it is not the Shayatin who have brought it down. Neither would it suit them nor they can (produce it). Verily, they have been removed far from hearing it.)(26:210-212)'' This saying is a good saying, and does not contradict those before it.
i think the ayyah is referring to the angels, not the humans, humans can touch the mushaf as the Quran is uncreated inshaAllaah !
i hope that makes sense
Assalamu Alaikum wa Rahmatullah