Lennon is absolutely right, and had not Lennon lended "I Want to Be Your Man" to the Stones back in their very early days, they may never have broken out in the first place.
As I recall, Lennon, McCartney and Jagger, et al, were hanging out in some London nightclub, and that's when Jagger had a personal revelation; "You mean, we can write our own songs?" To which Lennon replied; "Yeah, me and Paul will write one for you right now."
They then knocked out "I Wanna Be Your Man" in about half an hour and gave it to Jagger.