The exact nature of Burke's involvement (or lack thereof) is not yet clear in published reports, but one critical factor is missing in this report. Crux, I believe, says someone, presumably Burke, said Francis  approved the firing, which is not true. That would appear to be the foundation  of  Francis' powerful, immediate reaction.

BTW, your impugning the motive of hatred of Burke to  another is uncalled for, IMHO.