Schubert its generally known fact that not all songs credited to Lennon-McCartney were in fact written by both, especially in the latter years. Their arrangement was all songs the two of them did with The Beatles were credited to both, however many credited to Lennon/Mccartney were written solely by either Lennon or McCartney.
Other that that it is a pretty safe bet that the songs that were credited as written by one or more members of The Beatles were in fact. No shenanigan's there!
Regarding The Monkees, most all of their earlier songs were written by others and credited accordingly, but I believe many of their latter songs were in fact written by group members. Not to say that they may not have still had some help. Not sure about that.