To doubt the explanation, you'd have to come up with a reason somebody would alter the picture in such an obvious way, and what it got them.
The actual truth the "unaltered" picture with mike/stand would have told us was that it portrayed a female entertainer either talking or singing to the troops. Since "strippers" don't perform with microphones and stands on their stage, none of the readers would have thought that she was a stripper. But that "truth" would not have supported the salacious story the NY Times was trying to sell ie "strippers entertain the troops in Iraq"