Our Gemara on Amud Aleph tells us a harrowing story about Rabbi Tarfon, and how he was mistaken for a thief. In the end, he was released, but only because his captor found out he was the revered Rabbi Tarfon. This itself caused Rabbi Tarfon distress because he derived personal benefit from the crown of the Torah:

רַבִּי טַרְפוֹן אַשְׁכְּחֵיהּ הָהוּא גַּבְרָא בִּזְמַן שֶׁהוּקְפְּלוּ הַמַּקְצוּעוֹת דְּקָאָכֵיל. אַחֲתֵיהּ בְּשַׂקָּא וְשַׁקְלֵיהּ וְאַמְטְיֵיהּ לְמִשְׁדֵּיהּ בְּנַהֲרָא. אָמַר לוֹ: אוֹי לוֹ לְטַרְפוֹן שֶׁזֶּה הוֹרְגוֹ! שְׁמַע הָהוּא גַּבְרָא שַׁבְקֵיהּ וַעֲרַק. אָמַר רַבִּי אֲבָהוּ מִשּׁוּם רַבִּי חֲנַנְיָה בֶּן גַּמְלִיאֵל: כׇּל יָמָיו שֶׁל אוֹתוֹ צַדִּיק הָיָה מִצְטַעֵר עַל דָּבָר זֶה, אָמַר: אוֹי לִי שֶׁנִּשְׁתַּמַּשְׁתִּי בְּכִתְרָהּ שֶׁל תּוֹרָה.

The Gemara relates another incident: A certain man found Rabbi Tarfon eating figs from his field at the time when most of the knives (for cutting them down) had been set aside, (thereby indicating that the owners were now regarding the remainder left in the field as ownerless.) He placed Rabbi Tarfon in a sack, lifted him up, and carried him to throw him into the river. 

Rabbi Tarfon said to him: Woe to Tarfon, for this man is killing him. When that man heard that he was carrying the great Rabbi Tarfon, he left him and fled. 

Rabbi Abbahu said in the name of Rabbi Ḥananya ben Gamliel: All the days of that righteous man, Rabbi Tarfon, he was distressed over this matter, saying: Woe is me, for I made use of the crown of Torah, as Rabbi Tarfon was only released out of respect for his Torah learning.

This story contradicts a different version of the story about Rabbi Tarfon, reported in Maseches Kallah 5:2

שוב מעשה בר״ט שהיה אוכל קציעות מפרדס (שלו) בא האריס שלו ומצאו הכהו מכה רבה ולא אמר לו שהוא ר״ט עד שעמד אותו אריס והכיר בו כיון שהכירו קרע בגדיו ותלש בשערו היה צועק ובוכה ומתנפל לפני רגליו אמר לו אדוני מורי מחול לי. וכל כך למה שלא רצה להשתמש בכתר תורה שכל המשתמש בכתר תורה אין לו חלק לעולם הבא.

It is further related of R. Ṭarfon that he was once eating figs from his garden when his tenant came and [not recognizing him] gave him a severe beating. R. Ṭarfon did not disclose his identity until the tenant recognized him. On recognizing him, he rent his garments, tore his hair, cried bitterly and fell at his feet imploring him, ‘My lord master, forgive me!’ 

Why [did R. Ṭarfon not reveal his identity] all that [length of time]? Because he would not make use of the crown of the Torah, since whoever makes use of the crown of the Torah has no share in the World to Come.

This is a different outcome, as here Rabbi Tarfon does the right thing, and refuses to take any benefit from the crown of the Torah. 

This is not the only story about sages recorded in the Mishna, Gemara and Midrashim. It is easy to say Elu V’eylu (these and those are all words of the living God, that is, the Torah has different paths of expression and therefore different authentic opinions, see Eiruvin 13b) when it comes to halakhic discussions. However, how do we make sense out of contradictory rabbinic traditions of historical events? Aside from this story, the famous account of Rabbi Akiva’s life is substantially different, as recorded in three places, Kesuvos (62b-63a), Nedarim (50a), and Avos DeRabi Nosson (6:2):

In Kesuvos, the key elements of the story are Rochel marrying on the condition that Rabbi Akiva will study Torah, her father (Kalba Savua) disowning her and their resulting poverty and mesiras nefesh, and Rabbi Akiva studying away from home for twelve years, and then another twelve years.

In Nedarim, the key elements are similar, but there seems to be time spent as a married couple together before Rachel sends Rabbi Akiva off to learn Torah.

In Avos DeRabi Nosson, the key elements are Rabbi Akiva’s own awakening to study Torah after seeing how even water can eventuality bore through stone, his initial beginnings of humbly studying the Aleph Beis in Cheder (along with his son!), and studying in poverty for 13 years.

Rav Eitam Henkin Z”L (HY”D) in his essay on Rabbi Akiva’s life ( https://meyda.education.gov.il/files/Hemed/gan/lag2.pdf ), suggests that though there were competing traditions, each sugya chose the relevant features for its subject matter. The topic in Kesuvos is about sages who left home for extended time to study Torah. Nedarim discussed sages and their wives who lived in poverty to study Torah and were eventually rewarded. Avos DeRabi Nosson discusses the humble origins of persons who eventually grew  to be great sages.

Coming back to our contradictory accounts of Rabbi Tarfon’s adventures, the Chida (Kisse Rachamim) suggests that the incident in Avos DeRabi Nosson took place AFTER the incident in our Gemara. Rabbi Tarfon was then given an opportunity for tikkun, to repeat the nisayon and this time hold back from using the crown of the Torah. While this is a fairly typical resolution for disparities and contradictions used throughout Shas and commentaries, it’s more difficult to use regarding history. How plausible is it that “lighting strikes twice” and a similar event repeats itself? In addition, the language used in our sugya “All the days of that righteous man, Rabbi Tarfon, he was distressed over this matter.” כׇּל יָמָיו שֶׁל אוֹתוֹ צַדִּיק הָיָה מִצְטַעֵר עַל דָּבָר זֶה This indicated that Rabbi Tarfon never had a second chance for a do over. 

If we followed Rav Henkin’s model we can say that there were two competing traditions about Rabbi Tarfon. The subject matter of Maseches Kallah was Rabbi Tarfon’s financial mesiras nefesh, as there was another story brought before that which also discussed Rabbi Tarfon’s mesiras nefesh. The sugya in our Gemara discusses the idea of not misusing or misappropriating Torah honor, thus the other tradition is referenced.

It may feel disturbing to think that there was confusion about historical matters and important people such as Rabbi Akiva and Rabbi Tarfon. We must keep in mind, אין למדים מין האגדה Aggadah is not a source for Halakha (Yerushalmi Peah 2:4) therefore we do not have to expect the same standard of veracity as halakhic tradition. As a matter of faith, if it is recorded in the Gemara, we must not be cavalier about dismissing its “truth“, although, the truth and fine points about whether it occurred exactly as stated, may be less relevant than the lesson and mussar that the Gemara intends to teach. (Indeed, this is subject to a long-standing debate about how to interpret Aggadah, literally or allegorically.) Ultimately, perhaps it’s like all gedolim stories, they are inspirational, but we can take them with a grain of salt in terms of historical accuracy.