That portion of the documentary also aired on American television when McKuen appeared on Patti Gribow's PG Show. (The statement in question is at 1:49.)
I was extremely surprised—incredulous, even—when I heard this claim that McKuen and Cobain wrote something together, so I tried to find out more about this very unusual alleged collaboration between 1960s/70s pop poet Rod McKuen and grunge icon Kurt Cobain.
On his website, McKuen talks a little bit about Cobain but seems to contradict what he says in the video:
I was pleased that Kurt liked my work and the feeling was certainly mutual. He had a way of finding the unusual in every day things and writing about them in a very unique way. We had even kicked around the idea of writing something together. I had spoken with him on the telephone not long before his death so I was really stunned at the news. What a loss. To my way of thinking he was just beginning to find his legs as a songwriter.
The link between McKuen and Cobain is pretty tenuous, but a few examples exist, apart from their aforementioned telephone conversation.
Nirvana once half-assedly performed "Seasons in the Sun," a Jacques Brel song that McKuen adapted into English. The song was recorded by McKuen himself and the Kingston Trio in the 1960s but didn't become a hit until Terry Jacks recorded it in 1973. Cobain told interviewers that the song, which is sung from the perspective of a dying man, made him cry when he was a child, and Songfacts claims that Terry Jacks' version was the first record that the young Cobain ever bought. Nirvana's informal performance of "Seasons in the Sun" was included on the DVD that came with the 2004 Nirvana box set With the Lights Out.
Dave Grohl, in a satirical account of his first encounter with Cobain and Krist Novoselic, said, "Krist walked around with these poetry books by Rod McKuen, and Kurt would do interpretive dances while Krist recited Rod McKuen's poetry."
Charles R. Cross, in his book Here We Are Now: The Lasting Impact of Kurt Cobain, quotes a Boston Globe critic who described Nirvana's lyrics as "moronic ramblings by singer-lyricist Cobain, who has an idiotic tendency to sound like the Rod McKuen of hard rock."
That's the extent of their "collaboration." I hate to question McKuen's veracity, but there's no evidence that he and Cobain ever wrote anything together.
Cobain wasn't the only indie-rock guy to harbor a strange fascination with Rod McKuen. Yours truly has a big collection of McKuen's albums, and I even corresponded with him briefly in the 2000s when I was trying to arrange for Collectors' Choice Music to reissue some of his recordings. (Gordon Anderson from Collectors' Choice later started Real Gone Music, which reissued McKuen's albums Listen to the Warm and Sold Out at Carnegie Hall in 2013.) And Aaron Freeman, AKA Gene Ween, recorded an entire album of Rod McKuen's songs, Marvelous Clouds, in 2012.
I wish that Cobain had stuck around to write some songs with Rod McKuen. Frank Sinatra and Glenn Yarbrough recorded entire albums of McKuen's songs, and Madonna co-wrote a song with McKuen, so Cobain would have been in good company.