What is the basis for the claim that the entire New Testament can be reconstructed apart from original and copied manuscripts?

Bit of a mouthy title, but I remember reading a few years ago that the entire New Testament (perhaps with the exception of very few verses) and most of the Old Testament could be reconstructed from the writings of the early church fathers just because they had written so much about the Bible and referenced so many verses. To put it another way, if you took all of the writings of the early church fathers, pulled out every verse and reference, then put them together, you would have almost 100% of the New Testament and most of the Old Testament. Is this a new claim, or does it have its origins in a more distant past (say, older than a century)? Is the claim accurate? **What is the evidence for this claim?** (If the claim is technically false because the early church fathers didn't quote all that much, but technically true if a significantly longer time span is taken into account, then please say so.)