There is a simple way to fix that. You wouldn't want to force everyone to upload anyway (some are on metered connections etc.), so what you would do is offer a nominal discount for uploading, but if you choose it then you don't just host what you watch, you host whatever needs more hosting capacity. Then random third parties can't tell what you watch because what you host is random.
This reduces the efficiency somewhat, but it's easy to minimize that: Don't give someone a hundred movies to host, give them one movie and have them host it a hundred times (over the course of a year).