Basically, he proves, from the fact that Rabbi Chanina ben Tradion pronounced the name in order to teach it to his students, that they must not have had nikkud. Otherwise, he could have utilized a nikkud-based solution, before turning to a method that is so serious that Abba Shaul says that (in other situations) one who does this loses his share in the World to Come.
The gemara in question, from Avodah Zarah 17b-18a:
They then brought up R. Hanina b. Teradion and asked him, 'Why hast thou occupied thyself with the Torah?' He replied, 'Thus the Lord my God commanded me.' At once they sentenced him to be burnt, his wife to be slain, and his daughter to be consigned to a brothel.I have two issues with this proof.
(The punishment of being burnt came upon him because he pronounced the Name in its full spelling. But how could he do so? Have we not learnt: The following have no portion in the world to come: He who says that the Torah is not from Heaven, or that the resurrection of the dead is not taught in the Torah. Abba Saul says: Also he who pronounces the Name in its full spelling? — He did it in the course of practising, as we have learnt: Thou shalt not learn to do after the abominations of those nations, but thou mayest learn [about them] in order to understand and to teach. Why then was he punished? — Because he was pronouncing the Name in public. His wife was punished by being slain, because she did not prevent him [from doing it]. From this it was deduced: Any one who has the power to prevent [one from doing wrong] and does not prevent, is punished for him. His daughter was consigned to a brothel, for R. Johanan related that once that daughter of his was walking in front of some great men of Rome who remarked, 'How beautiful are the steps of this maiden!' Whereupon she took particular care of her step. Which confirms the following words of R. Simeon b. Lakish: What is the meaning of the verse, The iniquity of my heel compasseth me about? — Sins which one treads under heel in this world compass him about on the Day of Judgment.)
Firstly, even without nikkud, he could have told them Orally the words. He could have told them what the consonants were. Then, he could have told them another word with matching vowels. Or said, e.g., the Yud has a vowel as in the word Yerachmiel, or Yahalom, or Yom, and so on for the other letters. This is true whether or not they have orthographic signs.
Secondly, we might fight "kefirah" with "kefirah." Is all of this Amoraic? Or is some Savoraic or Setammaic? There are certainly signs of Savoraic influence here. (I'll put some other of my insights in the gemara in another post, beEzrat Hashem.) Specifically, "But how could he do so? Have we not learnt: The following have no portion in the world to come: He who says that the Torah is not from Heaven, or that the resurrection of the dead is not taught in the Torah. Abba Saul says: Also he who pronounces the Name in its full spelling? — He did it in the course of practicing" and all of this anonymous back and forth based on other sources certainly reads like stama digmara. If so, we might say that in fact he did not do it to "practice," or as Shadal reads it, "to teach his students." Rather, in general he pronounced Hashem's name.
But what about Abba Shaul? The answer is that Abba Shaul felt compelled to say this because people were doing it, and furthermore this is his opinion which he is adding on to the opinion of the Tanna Kamma. Say that Abba Shaul is a Tanna himself, and argues! And perhaps held like the Tanna Kamma. The problem with that if so, why is this a basis for punishment? Perhaps we might adopt the stama's answer that it was in public. Or perhaps we might say that he thought this, but he was wrong, and was punished for this.
If so, no one was talking about teaching to students, so no artifice was necessary, and no proof can be drawn from this story about the early or late origin of nikkud.