It exists independent of human awareness, but that doesnt mean we can't perceive it. It just means it doesnt rely on our awareness of it to exist. You're interpreting the sentence wrongly.
Also, it's not required you perceive all of reality in order to have glimpsed any of it.
Reality is not independent of perception. Perception is part of reality. Our perceptions are real. Reality is also a statement directly about perception. Without perception there can be no distinguishment between the real and the unreal, and the concept of reality would not exist. But its impossible for there to be a world without perception, so the whole discussion is flawed to begin with.