I think you’ve misunderstood. The library they constructed consists of fragments of antibodies. The antibodies come from mice, where they are generated (as usual) by random mutation and recombination of existing sequence. So they are random peptides. They got the antibodies from mice of two strains, one (and only one) of which is prone to autoimmune disease, which has previously been shown to generate catalytic antibodies more often than healthy mice. This is probably because mice normally have some mechanism for suppressing antibodies likely to attack the host, which has the side effect of suppressing catalytic antibodies; that mechanism is presumably defective in the autoimmune-prone strains. In other words, healthy mice normally suppress the random production of catalytic antibodies.
The reason for the enhancement in autoimmune-prone mice is speculative, and you could dismiss it. That won’t help you much, however, since healthy mice still produce catalytic antibodies (see https://www.pnas.org/doi/epdf/10.1073/pnas.92.6.2145, for example) – this would only buy you two orders of magnitude, not 40. In fact, if you read the body of the paper I cited, you’ll find that two of the five catalytic peptides actually came from the healthy mouse strain, so you have to give back those two orders of magnitude.
If catalytic peptides only occurred once in 10^50 times, then no probably no human would ever have produced a catalytic antibody. The reality is that they’ve been observed to occur multiple times in wha must have been a tiny number of humans screened for a small number of catalytic activities.
Axe’s number simply does not reflect reality.