This...isn't true.

Others have already said this, but the watermarking is something like "when the model flips a coin picking between two values, always choose heads". It was already flipping a coin. You're not choosing a less good result, you're just using a deterministic process when it was stochastic before.

This will have some impact on outputs, but unless you have some reason to believe that always picking tails was better than always picking heads (in which case, you should be working at one of these companies in model training!) it won't have any impact on output quality.