Why could Harry see thestrals after Cedric's death when in fact he didn't actually see the moment when Petigrew took his life?

I think it's もっと見る the fact that he was there when it happened, he heard it happen, he saw the body, and he understood death for the first time that leads to him seeing thestrals

when they say あなた have too "see" death it doesnt literally mean see it happen.

Because あなた see thestrals once you've seen death, and then accept that persons death. Harry hasn't yet accepted Cedric's death, which is implied in the 5th book when Dudley says that he hears Harry having dreams and he says things about how Cedric shouldn't die. But once Harry has accepted Cedric's death, he can see the thestrals.

He was told he could see them because he had been touched によって death, and, of course, he was touched によって his parents' deaths.

Actually this is a very good point. Harry didn't actually SEE Cedric's death since his eyes were shut. Hmm, this is one of those "wtf" moments I think.

The phrase "see death" is metaphoric. It really means to witness someone die and be old enough to understand what that means. Even though Harry didn't see Cedric's actual death, he'd heard the incantation and seen the flash of green light, he'd known what would happen, he'd even seen Cedric's dead body afterwards. That was enough for him to have "seen" death.