Well, I mean the really bad one was only 6 years ago. It does have a list of factories on its website, so I suppose it would be possible to find them. They use suppliers who presumably also supply everyone else (well, except those companies that run their own factories or have more specific sourcing arrangements) so I doubt you're more or less ethical than buying from any other major company. But that model does allow them a degree of latitude in dismissing concerns around a specific supplier.
There will be people sitting there weighing up the publicity potential of signing up to a specific ethical agreement, or using a particular sourcing arrangement against their price point on the high street. Which is presumably why they don't pay the living wage, why their sourcing is kind of... semi-transparent. I imagine they do send people over to inspect the factories they use, but I doubt they're asking many questions about fair wages, ability to unionise, working hours.
It is what it is... We don't have much choice in where we buy our clothes. But the idea that Primark is somehow holding an ethical line, that they're doing things right. That's bollocks.