I wouldn't advice trying the technical arguments ("the video could be faked!" etc) since the client is clearly unfamiliar with freelancing and these arguments would simply serve to confuse. Either 'yes' or 'no', the 'yes' having whatever caveats you want to go with it.
I've never freelanced, but I've spent a lot of time doing support, and I know what kind of personality is being dealt with here. The solution the poster has come up with is probably the best one apart from firing the customer (not always fiscally possible)
...since the client is clearly unfamiliar with freelancing...
That made me think of that cuatomer's employees and their working environment. I've read just the other day about a tech company over here that forces employees to have lunch at the company restaurant (with abusive prices) among many other outrageous measures. I'd say no to this kind of people, just because I don't want to make them any money.
I've never freelanced, but I've spent a lot of time doing support, and I know what kind of personality is being dealt with here. The solution the poster has come up with is probably the best one apart from firing the customer (not always fiscally possible)