It occurs to me, as I read this line, that Horatio is a sort of stand in for Shakespeare. We can imagine him as the writer of this play – attempting to clear Hamlet’s wounded name for him. It is, after all, the writer of this play who creates what lives behind Hamlet.
Of course, he also made him up. But if we look at Horatio – he does behave a lot like a writer. He observes. He watches. He listens. He asks questions. He is charged to tell this story – even if he must draw his breath in pain to do it.