Why would he allow them to record...
...what he was saying, while at the same time insisting they don't use it?
And then, why would they use it? It seems like the message is supposed to be that because he isn't flawless, he is somehow as bad as con men like Uri Geller. Randi doesn't represent that he never lies. What he encourages is the confidence that there is always an explanation. That reality is governed by knowable laws, and 'paranormal' events do not exist. Geller encourages people to disbelieve the truth, to indulge fantasy and pretend like anything they imagine is real. Randi is helping equip people to deal with the world and life - Geller is enabling people who use escapism to avoid it.
When Randi deceives, it's for someone's betterment, but the movie seems to present it as hypocrisy. It isn't.