If someone has developed the skills and can present a song well then I won't notice the book.

Fine. So they argument that someone with words on a sheet hasn't worked and internalized the song doesn't wash.

Maybe even they have the skill to only to need a prior glance through or a vague memory and then to read a verse ahead. I have watch someone read a story to a child and, first time through, read ahead and alter bits that maybe too frightening at bedtime. As Jack Campin has indicated it only takes practice to sing a hymn reasonably on sight, sorting out the scanning of the words ahead of time. These days (and its mainly funerals for many of us) one also has to spot where the familiar text has been made gender neutral and how - try that without book in hand.