That's about right. The basic principle was that the writing should have been written by an apostle or close disciple of an apostle. So when people disagreed over whether a certain text should be in the canon, it was often because they disagreed over authorship. In the third century, Dionysius, patriarch of Alexandria, analysed the book of Revelations and concluded that it wasn't by the same author as the Gospel or letters of John. He therefore argued that it should not be considered canonical.
Of course, people in antiquity tended to assume that a book was written by the person whose name was attached, even with the most obvious forgeries. This is a bit surprising given how very common the practice of pseudepigraphy - that is, writing a text and claiming that some great worthy of the past was the author - was in antiquity. Think of how many texts there are supposedly by Plato, Aristotle, and any number of other worthies, even before you consider the Christian pseudepigrapha. Sometimes different texts attacked each other, more or less explicitly: look at
2 Thessalonians 2:2, which apparently attacks some other letter supposedly written by Paul (and note 3:17, which offers a way of ensuring that
this letter is genuine). Of course this is rather ironic, given that many scholars think that 2 Thessalonians is actually itself pseudepigraphical - basically, the author is protesting too much that he is really Paul! In this case, the "fake" letter attacked in 2:2 would be 1 Thessalonians - which
is by Paul!
Nevertheless, it didn't entirely revolve around authorship. Thus, the book of
Hebrews is anonymous, and no-one knew who had written it. Many people suggested Paul (and, traditionally, it is identified as Pauline) but even in antiquity there was no agreement on this. As a result, Hebrews was not used in many churches until after the fourth century, when it
was included in the canon. Thus, the intrinsic quality of a book was also apparently a factor.
Of course, you must bear in mind that the notion of a "canon" at all was something that developed only gradually. In Jesus' day, all Jews venerated ancient Jewish texts, but there was not a sense that some were specially "canonical" and the others were just old. That was a distinction that came about only after the Council of Jamnia at the end of the first century AD. Similarly in Christianity, the word "canon" meant not a collection of texts but the whole doctrinal, ethical, and liturgical tradition of the church, taught by Jesus to the apostles and established by them in the churches that they set up. This is how Irenaeus and Tertullian, at the end of the second century, use the word. In their minds, the writings of what would become the New Testament are authoritative because they reflect that tradition and are part of it. Of course, to show that they must also show that many of the writings apparently from that period are inauthentic - thus Irenaeus devotes much time to showing that there have to be precisely four Gospels, no more and no less, to exclude all the weird Gnostic ones.
So it's only after the 390s, when the canon of the New Testament was officially established, that you really get the sense of a "canon" of
writings as opposed to that broader sense. But it wouldn't be until the Reformation that the stronger notion developed that the textual "canon" and the "canon" of tradition might actually be
rival authorities, rather than
complementary ones - that is, that church teaching and the Bible might be at odds with each other.
Again, you can get more information on all of these books (canonical and apocryphal) at
www.earlychristianwritings.com, complete with possible dates and discussions of authorship, and all probably much more reliable than anything I might say.