Re: Under what law, exactly?
You're absolutely right - there is no such law.
The copyright on a photo of you remains with the photographer (or whomever they sell/grant it to), not you - you have no legal rights to your own face because it is, by definition, in the public domain.
But people are not only utterly clueless about copyright law but, furthermore, also believe in the fairytales of 'fair use'; to which I say "go and sample one, single beat by James Brown and see what the lawyers do to you - I refer you to The Shawshank Redemption's observation regarding the effects of being cast down with the sodomites."
They think that they can circumvent it by re-recording movie dialogue themselves.
They think that '5%' (or however much they erroneously believe) is legal.
You name it, they believe it - except, ironically, the one true fact of the matter that is that there is a copyright on something the second it is created whether anyone registers that copyright or not and the only reason for registering it (or giving a sealed envelope to your solicitor/bank manager) is to make it easier to prove that you are the owner of said copyright later.
People are ignorant and they like being ignorant - it means they can make fairytales up in their heads rather than make the effort to investigate matters and educate themselves.