That's a completely valid point to make.However,I believe that appeals courts are more sensitive to "bias" (my word) that could *increase* a defendant's chances of being convicted,not one that *decreases* the chances.
I'm no lawyer and have no experience in either civilian or military law so someone who *has* such training/experience may well disagree.
If the defendant goes to a newspaper and does an interview, saying, for example, that he killed someone, he can’t later demand a change of venue because people think he killed someone.
In this case, the defendant, knowing the totality of the circumstances of his actions, chose to go to the White House and have the president speak on his behalf as well as making his own comments. Such actions invite commentary, and of course, commentary can reasonably be anything (I think he’s innocent, I think he’s a traitor, I think he’s a moron, etc.)