רש"י במדבר ט"ז:א' ד"ה דתן ואבירם. ... מֶה עָשָׂה? עָמַד וְכָנַס ר"נ רָאשֵׁי סַנְהֶדְרָאוֹת — ... וְהִלְבִּישָׁן טַלִּיתוֹת שֶׁכֻּלָּן תְּכֵלֶת, בָּאוּ וְעָמְדוּ לִפְנֵי מֹשֶׁה, אָמְרוּ לוֹ טַלִּית שֶׁכֻּלָּהּ שֶׁל תְּכֵלֶת חַיֶּבֶת בְּצִיצִית אוֹ פְטוּרָה? אָמַר לָהֶם חַיֶּבֶת, הִתְחִילוּ לִשְׂחׂק עָלָיו, אֶפְשָׁר טַלִּית שֶׁל מִן אַחֵר חוּט אֶחָד שֶׁל תְּכֵלֶת פּוֹטְרָהּ, זוּ שֶׁכֻּלָּהּ תְּכֵלֶת לֹא תִפְטוֹר אֶת עַצְמָהּ?! (תנחומא):
... What did he [Korach] do? He arose and assembled 250 men, fitted to be heads of the Sanhedrin... and he attired them in robes of pure purple wool. They then came and stood before Moses and said to him, “Is a garment that is entirely of purple subject to the law of Zizith or is it exempt”? He replied to them: “It is subject to that law”. Whereupon they began to jeer at him: “Is this possible? A robe of any different coloured material, one thread of purple attached to it exempts it, and this that is entirely of purple should it not exempt itself (i.e. ipso facto be exempt) from the law of “Zizith”? (Midrash Tanchuma, Korach 2).
Why are Korach and his followers asking whether it is Chayav in Tzitzis? There is no reason why it shouldn't be Chayav in Tzitzis (strings at the corner). All that they've proved is that it should be Patur from Techeiles. Why don't they ask him whether a Beged that is completely Techeles should be Chayav in having Techeiles strings?