I don't know how this is implemented in UI's but it seems that this rehosting occurs too easily.
If you visit someone's page and then.. oops its inappropriate.. I have to take quick action now before I get sued (and its easy to make mistakes and overlook something)
I'd rather have an explicit opt-in button 'Rehost' (or something) than having to opt-out by clearing the cache.
Or is this easily configurable already?
So yes, users have complete control over what content they are serving.