> For me QA is tasked with making sure that the product functions as intended. that means coming up with clever test suites to explore the spaces that the developers didn't think to, making sure the coverage for operational problems is adequate, and also long term tracking of performance and memory utilization.

This pretty much. My last job didn't really have QA so I did the next best thing which is writing a bunch of integration tests for the use cases that matters for the product. They were not an indication for correctness, but more like a canary to warn me if I break something while developing. Bugs reported by consumers usually warn me of area not well covered.

QA would play the same whole. They shouldn't need to check for code correctness, their most useful task is to surface bugs that breaks the product requirements (performance, security, business logic,...). And for that, having knowledge of the implementation is unnecessary. In the above example of writing integration tests, I took care of only using the public interface of the modules.