Well, it's sort of true, but it isn't as simple as that. Under the terms of the Royal Marriages Act, which goes back to the reign of George III in 1772, if he married without the Queen's consent when under 25, the marriage would be illegal and invalid; if the Queen doesn't give consent, there's nothing he can do. Once he's 25 and wants to marry without the Queen's consent, there is a way to do it, but it isn't easy. He has to give notice to the Privy Council of his intention to marry and then wait for a year. After the year is up, he can marry as long as Parliament hasn't passed an act during that year forbidding the marriage.
So, yes, if he's prepared to go through the formality of giving notice to the Privy Council, waiting for a year, and risking that Parliament won't intervene and probably cause a constitutional crisis in the process, he can marry without the Queen's consent. But it's by no means as simple as just saying "up yours, Granny," and skipping off to the nearest village church.