The (linked) Midrash Tanchumah says as follows:
אמְרוּ לָהֶם, הֵיכָן אַהֲרֹן. אָמְרוּ לָהֶם, מֵת. אָמְרוּ לָהֶם,
הֵיאַךְ מַלְאַךְ הַמָּוֶת יָכֹל לִפְגֹּעַ בּוֹ, אָדָם שֶׁעָמַד
בְּמַלְאַךְ הַמָּוֶת וַעֲצָרוֹ, דִּכְתִיב: וַיַּעֲמֹד בֵּין הַמֵּתִים
וּבֵין הַחַיִּים וַתֵּעָצֵר הַמַּגֵּפָה (במדבר יז, יג). אִם אַתֶּם
מְבִיאִין אוֹתוֹ, מוּטָב. וְאִם לָאו, נִסְקֹל אֶתְכֶם
When they [Moshe and Elazar] descended from the mountain, they said to
them, "Where is Aharon?", They said "He died", They said to them "How
can The angel of death have touched him?!!, He is the person who stopped
the angel of Death, as it states "And he [Aharon] stood between the
live and the dead, and the plauge stopped, (Bamidbar 17:13), If you
bring him good, if not we will stone you!"
We see from the context, that they did not suspect that Moshe killed Aharon, but rather that Aharon was still alive, and that Moshe had "kidnapped" him.
It may be that the "stoning" which they threatened Moshe with, was not necesarrily by any halachic law of Moshe being deserving of the death penalty of stoning, but in their rage and fury, they threatened him with stoning.