I think you assume incorrectly (but it is a good discussion)...I don't think Davis questioned at all Cleburne's patriotism, but seemed aghast at the Cleburne proposal of arming slaves. Davis was prejudiced against giving high command to those who were not of the West Point upbringing militarily. (Forrest was not West Point, but was given an independent command, but not a whole army.) Also Cleburne was a signer of petitions against Bragg, something to not be forgiven by the spiteful Davis. Bragg said that “We must mark the men”, and “agitators must be watched” after he go kicked upstairs to the Davis cabinet. Read correspondence between the principle players in the Cleburne proposal, and it gets intense. (W.H.T. Walker got pretty emotional about the proposal, he didn’t like it!)
Authors of book about Cleburne seem to be of the opinion that Cleburne got passed by more from not having a West Point education.