Certainly much of it is cynical manipulation. During a war you say the worst things you can about your enemy; the worst you can get away with. Make sure ingroup is as hysterical as possible about outgroup. To start with, Fascism is always especially xenophobic and anti-cosmopolitan.
However, the way and style in which they immediately jump to accusations of a coup is revealing their own internal paranoia. They're well aware they should have provoked a proper full-contact coup attempt. They're well aware they've done many things to deserve being thrown down. They are presenting this stuff as a great threat because it feels, to them, greatly threatening. So much so that even yoinking a ceremonial podium is threatening enough to possibly collapse the allegedly "rational" regime.