I don't think there's a direct link to the tokenizer - it's a higher level capability. You can stitch together a nonsense word out of common "word fragment" tokens and see if that impairs the LLM's ability to recognize the word as nonsense.
The "capability" you see is for the LLM to recognize its a human typed random string since human typed random strings are not very random. If you send it an actual random word then it typically fails.