As I recall, one of Miko's ambitions is to be made leader of the Human Village- a position that does not currently exist, and which all of the youkai factions would take umbrage at. Since part of a youkai's existence is tied to its awareness of its own existence, spiritual possession is far more damaging to them than to humans. Perhaps Miko wants the various groups to believe that Mizuchi is on a rampage again so that she can offer her "protection" (i.e., bring her under her control as a tool to destabilize the youkai).
But that's a bit murky, even for Gensokyo's standards.