This is not true. It would be for most casinos, but not Stake.
You won't be required to KYC in order to withdraw, only to continue playing. Unless you're suspected of cheating or scamming some how, when they decide to KYC you, they put your account in withdraw only mode - you're still able to withdraw your balance whether you decide to send in the docs or not.
Really, haven't heard of the withdraw only mode? It is a cool thing that they do this, but it doesn't really makes sense in my eyes. If they have doubts that your bets or casino play is suspected, why would they still allow to withdraw that money? Asking KYC and later on approve withdrawal is more logic!