The history there is that Australia used to have a government run monopoly on telephone infrastructure and services (Telecom Australia), which was later privatised (and rebranded to Telstra). The privatisation left Telstra with a monopoly on the infrastructure, but also a requirement that they resell the last mile at a reasonable rate to allow for some competition.
So Australia already had an existing industry of ISPs that were already buying last mile access from someone else. The NBN was just a continuation of the existing status quo in that regard.
> They even have a grey fibre box that looks identical to the NBNCo box except it's labelled LBNCo with the same font
Early in my career I worked for one of those smaller telcos trying to race to get services into buildings before the NBN. I left around the time they were talking about introducing an LBNCo brand (only one of the reasons I left). At the time, they weren't part of Opticomm, but did partner with them in a few locations. If the brand is still around, I guess they must have been acquired at some point.