No, I don't see his rejection of the correspondence theory having anything to do with a conflation between something being true, and our knowing something is true.

I think he's just endorsing the standard objection to correspondence theory, which doesn't really have much to do with how we know something is true, it is more about what constitutes a good theory (of truth or of anything else).

So if your theory of truth is something like "X is true if X corresponds to reality", the objection is that "corresponds to reality" is something like a synonym for truth rather than a theory of truth. It doesn't give us the sort of insight into truth we'd want for something to be rightfully deemed a theory of truth.

This is a little bit of a stretched analogy but I don't mean it to be exact, just to roughly get the idea across: If I offered a "cougar theory of mountain lions" that was like "X is a mountain lion if X is a cougar", that wouldn't be much of a theory. I'm just substituting two terms that refer to the same animal. A theory of mountain lions might be something like "X is a mountain lion if X is a large predatory cat species native to America.... etc etc." The objection to the correspondence theory of truth is that it is something like my "cougar theory of mountain lions".

So while it is true that cougars are mountain lions, that's not a good theory of mountain lions. Similarly, in the beginning of the video Blackburn says that while its perfectly correct to say that "x is true if x corresponds to reality", that is insufficient for a theory of truth.