Some people do not believe that anyone who knew Jesus directly -- whether his followers or his family -- were involved in writing any of the documents that were eventually accepted as part of the New Testament. It is commonly assumed that it was a standard thing for people to forge writings in the name of famous people, and of course the early church would have accepted any writing uncritically if it had the name of an apostle attached to it, or one of Jesus' family.
While there were plenty of documents falsely written under the name of someone famous in the early church, it does not follow that the early church would accept them uncritically. In fact, we know that they did not. There are quite a few writings with the apostles' names attached which were rejected by the early church as pseudonymous forgeries. Again Bart Ehrman, no friend of orthodox Christianity, has collected some of these works in his book Lost Scriptures: Books that Did Not Make It into the New Testament. Here we see 5 works ascribed to Peter (as opposed to 2 in the New Testament) and one more mentioning both Peter and James, 3 that drop the name Thomas in the title (none in the New Testament), 9 others variously claiming a connection to James, John, Philip, Mary, or Paul. One writing even claims co-authorship of eleven surviving apostles (John, Thomas, Peter, Andrew, James, Philip, Bartholomew, Matthew, Nathaniel, Judas Zelotes, and Cephas) -- which would form something of a mandate to accept and propagate the writing as coming from the best possible sources on Jesus ... if it were considered genuine.
Once again, Mr. Ehrman has provided a valuable service by showing just how often dropping the name of a famous figure of early Christianity -- even a follower or a relation of Jesus -- was not enough to persuade the early church to accept a writing. The early church also wanted some assurance that it actually came from the named source. Apparently, they were aware that some people might resort to forgery to promote their own views and wanted some guarantee of authenticity. It is a fair question what, exactly, their methods were; but to say they were swayed by mere name-dropping is disproved by how many texts with big-name attributions were regarded as forgeries in the early church.
In the companion volume Lost Christianities, Ehrman provides a chart with approximate dates for these non-canonical writings. By examining it, particularly with an eye to which writings claimed a connection to followers and family of Jesus, the reader may gain another useful clue as to why the early church did not necessarily accept these documents as coming from the claimed sources. Per Ehrman's chart, these rejected documents have conspicuously late dates compared to the lives of the supposed authors. They were written no sooner than the second century, quite a few not until the middle of the second century, the third century, or in one case even the fourth century for a document claiming to come from Paul. It seems reasonable enough, on the surface, that documents that were never heard of by the first few generations -- or centuries -- of Christians might be suspect whether they were really from the apostles. While I don't recall Dr. Ehrman anywhere drawing attention to the reasonable suspicion of authorship that would fall on a document written centuries after the supposed author's death, the early church seems to have been well aware of a chronological problem here with the historical plausibility of the claim.