This is a matter of perception. I don’t think the White house is behind this in any way, but it needs to publicly distance itself from Thibault and others who take this tack. When stuff like this happens, there’s always the danger that the public will perceive it as an example of “will no one rid me of this turbulent priest?”
I see signs of disaffection among military supporters of the president because of seemingly minor things like this. I remember cringing during the Republican convention when delegates were sporting the “purple heart band aids.” No matter that it was designed to mock Kerry’s alleged minor wounds, people who had received the award didn’t think. It conveyed the impression that people who were running this show didn’t understand that soldiers might believe they were mocking them.