Rashi on Korach's claims:
וּמָה רָאָה קֹרַח לַחֲלֹק עִם מֹשֶׁה?
נִתְקַנֵּא עַל נְשִׂיאוּתוֹ שֶׁל אֱלִיצָפָן בֶּן עֻזִּיאֵל,
שֶׁמִּנָּהוּ מֹשֶׁה נָשִׂיא עַל בְּנֵי קְהָת עַל פִּי הַדִּבּוּר
From this explanation, Korach did accept Moses and Aharon's roles and their leadership and only questioned other positions within the tribe of Levy, specifically Elitzafan as the supervision. So why was Korach's Machlokes so dramatic?
As we see in the beginning of Bemidbar the Nessi'im were clearly G-d chosen and I don't see Korach questioning G-d in His decisions.
Were the whole mess and the death of close to 15 thousand Jews justified by such a minor disagreement?