My data includes shuttered hedge funds, but you're right that poor performance is systematically underreported because managers either cease reporting to databases, or never report failed start-up funds.

Depending on your assumption about the magnitude of survivorship bias, you might conclude that hedge funds have just as poor of an overall track record as mutual funds. While my view isn't that extreme, I do find that the majority of hedge funds don't demonstrate alpha when appropriately benchmarked.