the fact that the BMBL's biosafety levels were influenced by the NIH levels P1-4 (but it seems pretty obvious since they're quite similar and both developed at least partly by the NIH)
whether the idea of 4 biosafety levels existed before Asilomar (but I haven't found any evidence that it did, and looking through the history of ABSA conferences the first references to biosafety levels I could find were post-Asilomar. This source claims without citation that the idea of 4 levels originated in the mid-1970s, which was when Asilomar happened)
re: "One language model claimed that standards such as BSL-4 originated with the Asilomar conference on recombinant DNA", I found some evidence for this.
The summary statement of the Asilomar conference recommends 4 levels of containment depending on the risk of the experiment. They sound similar to today's BSL 1-4.
A history of the NIH guidelines for working with recombinant DNA makes it clear that they were heavily influenced by the Asilomar conference.
I haven't found sources for: