Was Rabbi Yaakov the grandson of Acher?

Yesterday we finished mashechet Chullin in Daf Yomi, and there (Chullin 142a), Rav Yosef asserts that the Tanna Rabbi Yaakov was the grandson of Acher, that is, Elisha ben Avuya,

As background, while the Mishna (Rabbi Meir) implies that Biblical verses discussing reward of long life for fulfilling precepts were meant literally, about life in this world, a brayta has Rabbi Yaakov explaining this as referring to reward in the world-to-come. According to the Munich manuscript and various Vatican manuscripts, as well as Rashi, the gemara ends there. But there is a haavara -- a transferred sugya -- from a gemara in Kiddushin 39b.

There, we see an incident of one who was sent by his father to send away the mother bird and died while descending. Thus, the verse cannot be taken literally. The gemara proceeds to suggest that this was an actual, rather than theoretical incident. After a long discussion, the gemara in Chullin ends:

אמר רב יוסף אלמלא דרשיה אחר להאי קרא כרבי יעקב בר ברתיה לא חטא מאי חזא איכא דאמרי כי האי מעשה חזא ואיכא דאמרי לישנא דרבי חוצפית המתורגמן חזא דהוה מוטלת באשפה אמר פה שהפיק מרגליות ילחוך עפר והוא לא ידע למען ייטב לך בעולם שכלו טוב ולמען יאריכון ימיך בעולם שכולו ארוך:

Rav Yosef said: Had Aḥer, literally Other, the appellation of the former Sage Elisha ben Avuya, interpreted homiletically this aforementioned verse: “That it may go well with you” (Deuteronomy 5:16), as referring to the World-to-Come, as did Rabbi Ya’akov, the son of his daughter, he would not have sinned. The Gemara asks: What did Aḥer see that led him to heresy? Some say that he saw an incident like this one witnessed by Rabbi Ya’akov, and some say that he saw the tongue of Rabbi Ḥutzpit the disseminator, which was cast in a garbage dump after he was executed by the government. Aḥer said: Will a mouth that produced pearls of wisdom lick the dust? But he did not know that the phrase “that it may be well with you” means in the world where all is well, and that the phrase “that your days may be long” is referring to the world that is entirely long.

This is a great illustration of the motivating factor behind Mi Vami. Elisha ben Avuya became an apostate because of a specific incident, either the same (sort of) incident discussed earlier, or a similar one.

If so, perhaps we can understand that this personal history was what drove Rabbi Yaakov to his interpretation. As a grandson of Elisha ben Avuya, yet a religious man, he could not take the verse at its surface sense and yet could not dismiss Divine reward and punishment. He grappled with it and arrived at this interpretation.

However, I would point out that Rav Hyman in Toldot Tannaim veAmoraim dismisses this relationship. He writes:

That is, he asks where Rav Yosef got this biographical information, since there is no other reference to it in the Talmud. He dismisses the idea that this could have been a received tradition. More compellingly, he points out an incident in masechet Chagiga, where Rabbi Yehuda HaNasiwas approached by Acher's daughter, asking to be provided for. Rabbi Yehuda HaNasi expresses surprise that there are descendants of Acher out and about. Yet, Rabbi Yehuda HaNasi was a student of Rabbi Yaakov, so why would he be surprised. Rav Hyman points out that a parallel Yerushalmi omits the words bar bartei, "the son of the daughter of". He concludes that this was a girsological error, and really the text read bar Karshay, which is the patronymic of Rabbi Yaakov.

If so, the familial / scholastic relationship has no bearing on the developed positions in this sugya.