You say that the tract doesn’t say that an accurate text=accurate history. It’s true that it doesn’t say so in so many words. But after the section on textual accuracy, ending “we can work from it with confidence,” the tract goes on immediately to say "Next we take a look at what the Bible, considered merely as a history, tells us. . . "
I disagree. here is the relevant text of what I posted, and I will insert my comments and highlight key text in red.
The Catholic method of proving the Bible to be inspired is this: The Bible is initially approached as any other ancient work. It is not, at first, presumed to be inspired. From textual criticism we are able to conclude that we have a text the accuracy of which is more certain than the accuracy of any other ancient work. [Up until this point, all that CA has said is that the text we have today accurately represents what the original author wrote.]
Next we take a look at what the Bible, considered merely as a history, tells us, focusing particularly on the New Testament, and more specifically the Gospels. We examine the account contained therein of Jesus’ life, death, and resurrection. [Here, CA is specifying that we must examine the details of Jesus’ life as they are recorded in the Gospels. *Why we are concerned about this information is about to be explained.]
Using what is in the Gospels themselves and what we find in extra-biblical writings from the early centuries, together with what we know of human nature (and what we can otherwise, from natural reason alone, know of divine nature), we conclude that either Jesus was just what he claimed to be—God—or he was crazy. [Here we arrive at the doorstep of the Trilemma Argument. Dawkins’ fourth “L” - Jesus the Legend - has been ruled out by historical evidence from “extra-biblical writings” that the tract mentions.
From this point on, the Spiral Argument has smooth sailing. The Trilemma Argument is well-known and easily defended. Jesus is Lord.
Further, He promised to build a Church. The Church which God built cannot teach error. Finally, an infallible Church tells us that the Bible is not merely historically accurate, but also infallible.
Dr. Peter Kreeft begins with a similar approach in an article on the resurrection:
We believe Christ’s resurrection can be proved with at least as much certainty as any universally believed and well-documented event in ancient history. To prove this, we do not need to presuppose anything controversial (e.g. that miracles happen). But the skeptic must also not presuppose anything (e.g. that they do not). We do not need to presuppose that the New Testament is infallible, or divinely inspired or even true. We do not need to presuppose that there really was an empty tomb or post-resurrection appearances, as recorded. We need to presuppose only two things, both of which are hard data, empirical data, which no one denies: The existence of the New Testament texts as we have them, and the existence (but not necessarily the truth) of the Christian religion as we find it today.
peterkreeft.com/topics-more/resurrection-evidence.htm
At no point does it again consider the question of historical accuracy.
Nor does it need to do so in order to make its case. The tract is brief, perhaps overly so on this one point, but it points to extra-biblical writings which corroborate the Gospels.
If the reader does his homework by examining this evidence, he will come to the conclusion that the New Testament books are historically reliable. Since one of these books, Matthew, speaks of the foundation of a Church, the chain of the argument is unbroken.