I think the hypothesis is interesting but much too simplistic an
explanation for the development of the Gospels. Apparently there was an
array of "Jesus said" writings during the latter 1st century of Gospel
authorship and editing. I am one who believes that a very early account
of sayings was written down by one of the disciples (probably cousin Matthew)
and was foundational to later interpolations. This "sayings gospel" may have
been seminal to QI, QII, the Gospel of Thomas, etc.
The 2NH does not seem to take into account a variety of "memoirs" that
circulated among the Yeshuines that were later embedded in "Christian" gospels.