I never said the Gospels were fraud. They merely were not written by Luke, Mark, Matthew or John. Nobody knows who wrote them and only approximately when.
Obviously no one can prove shit about the authorship of the gospels.
What we can do is look at evidence and make inferences.
You have provided no previous rationale for believing the authorship of the gospels are fraudulent. It's definitely possible, but up until now you haven't made the case.
I've given multiple lines of evidence. Even a skeptic like Bart Ehrman says we have to take seriously Bishop Pappas' report that two of the canonical gospels are attributable to Matthew and Mark, although we can't know for sure.
Not one source from any Biblical scholar I’ve read says anything about “reasonably be inferred”.
I am doing my own logical inference based on what I've read from reputable scholars.
These apostles came from an area that was overwhelmingly uneducated and illiterate. They were simply incapable of writing those gospels in their own language, much less Greek.
People who read the elegant prose in the King James Bible are quick to leap to the conclusion that obscure citizens of the Roman Empire couldn't write that eloquently.
The NT authors wrote in a simple and basic Koine Greek. Later transistors stylized the language into fancy Elizabethean English.
Luke was a Greek speaking gentile, and supposedly a doctor.
Matthew was a tax collector.
Mark seems to have been a Hellenized Jew who wasn't from Palestine. It's in the realm of possibility he could have composed his testimony in Aramaic which was later translated and edited into Koine Greek.
Jesus was a Rabbi who undoubtedly had some education in reading Hebrew.
It's an assumption that these were all illiterate peasants, although that is definitely possible. And I am almost certain a fisherman like Peter was illiterate.
Wrapping up, there would be nothing to stop John or Matthew telling their testimony to Hellenistic Jews who could write Greek. That area of the world was deeply Hellenized.