Because it won't be in the training directly. It is applied after a model generates its distribution of likely tokens, biasing each token randomly based on a random key and unrelated to any meaning of the words. So half the time, the most likely token becomes more likely and half the time it becomes less likely, and the same for every other token (when temperature is above 0).

You then look at the tokens actually picked to see how closely they follow this pattern that isn't connected to the meaning of the tokens. With enough text, you can then analyze the chance of it happening by chance verses being because the generation of the tokens was done using the algorithm, and you can save a positive result until you are arbitrarily sure. There is a chance of a false positive, but the chance of a false positive approaches the chance that the murderer happened to have fingerprints that matched your and both forensics labs happened to have mixed up the dna tests and the eye witness happened to misremember the face and your phone gps happened to glitch out and put you at the murder scene at the time of the crime all happening. It is theoretically possible only in the same sense that quantum teleporting a cat is theoretically possible.

The real question is how much text do they need for a given level of certainty and what do they check for. If they flag a positive at a p value <.01, that's a problem. If they can reasonably get a p value of < 1e-12 in only a few paragraphs of text, that is effectively no false positives (but a lot of 'too short to analyze' outcomes).