I think the correspondence theory's thesis "'p' is true iff p is the case" only makes sense understood as a grammatical remark. It'd state something like you can't say "'p' is true" and "'p' is not the case" simultaneously.

There seems to be a logical link between "being true", "being a fact", "being asserted" and "being believed". If I assert p, then I'm forced to say that p is true, that p is a fact, and that I believe that p. All these statements are indissociable from the first person, and that's the whole thing the correspondence theory's formulation points to.

I can hardly understand the metaphysical thesis that there is in the world, beyond our practices, a brute fact that makes a statement true.