This was my first reaction as well. In addition to the valid reason you mentioned, I think that if this gets around it potentially damages one of the primary reasons that a candidate might be interested in the Saints and be willing to overlook our football-related deficits relative to other openings. Loomis has demonstrated a lot of loyalty to coaches and players during his tenure in the face of difficult circumstances (on and off the field). A coach wants to know that the GM has their back and is on the same page with ownership in key organizational decisions. Loomis (if what DA said is true) unnecessarily castrated himself by volunteering that he didn't want to fire DA and was overruled by an owner that doesn't really otherwise meddle in football decisions and is fairly green as it relates to football operations.
I've not been one to jump on the "fire Mickey" bandwagon by any means, and I'm still not there, but making a statement like that offers nothing but downside. He should know better. Hope it doesn't cost us.