This is an unfounded objection because: The gospels were written in the style of Greco-Roman historical biography.1 As with all biography of this style it was customary to mention any sources that were used to write the work, which the gospels do.2 Internal evidence within the text shows that these books of the New Testament were originally pinned before the eye witnesses of Jesus’ life had died. Since the New Testament was written by eyewitnesses during the lifetime of other eyewitnesses it means that the information was falsifiable.
The early date of the original documents ensured corroboration from other surviving witnesses. Scripture is even specific enough as to give us a number of eyewitnesses to the resurrected Christ when it says in 1 Corinthians 15, “After that, he appeared to more than five hundred of the brothers and sisters at the same time, most of whom are still living, though some have fallen asleep.” Luke, in explaining why he wrote his gospel, used the words eyewitnesses, orderly account, and that you may know the certainty. It’s clear from reading these authors that they claim to not only be eyewitnesses, but that they enjoyed the corroboration of hundreds of other eyewitnesses.
1 Aune, DE. “The New Testament in Its Literary Environment.” books.google.com (1988): 64.
2 Burridge, RA. “What Are the Gospels?: A Comparison With Graeco-Roman Biography.” books.google.com (2004): 198.